(THIS IS IN C LANGUAGE)

4.27 (Pythagorean Triples) A right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the hypotenuse. Find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 500. Use a triple-nested for loop that simply tries all possibilities. This is an example of brute-force computing. Its not aesthetically pleasing to many people. But there are many reasons why these techniques are important. First, with computing power increasing at such a phenomenal pace, so- lutions that would have taken years or even centuries of computer time to produce with the tech- nology of just a few years ago can now be produced in hours, minutes or even seconds. Recent microprocessor chips can process a billion instructions per second! Second, as youll learn in more advanced computer science courses, there are large numbers of interesting problems for which theres no known algorithmic approach other than sheer brute force. We investigate many kinds of problem-solving methodologies in this book. Well consider many brute-force approaches to vari- ous interesting problems.

(3,4,5):9+16=25 (4,3,5):16+9=25 (5,12,13):25+144=169 (6,8,10):36+64=100 (7,24,25):49+576=625 (8,6,10):64+36=100 (8,15,17):64+225=289 (9,12,15):81+144=225 (9,40,41):81+1600=1681 (10,24,26):100+576=676 (11,60,61):121+3600=3721 (12,5,13):144+25=169 (12,9,15):144+81=225 (12,16,20):144+256=400 (12,35,37):144+1225=1369 (13,84,85):169+7056=7225 (14,48,50):196+2304=2500 (15,8,17):225+64=289 (15,20,25):225+400=625 (15,36,39):225+1296=1521 (15,112,113):225+12544=12769 (16,12,20):256+144=400 (16,30,34):256+900=1156 (16,63,65):256+3969=4225 (17,144,145):289+20736=21025 (18,24,30):324+576=900 (18,80,82):324+6400=6724 (19,180,181):361+32400=32761 (20,15,25):400+225=625 (20,21,29):400+441=841 (20,48,52):400+2304=2704 (20,99,101):400+9801=10201 (21,20,29):441+400=841 (21,28,35):441+784=1225 (21,72,75):441+5184=5625 (21,220,221):441+48400=48841 (22,120,122):484+14400=14884 (23,264,265):529+69696=70225 (24,7,25):576+49=625 (24,10,26):576+100=676 (24,18,30):576+324=900 (24,32,40):576+1024=1600 (24,45,51):576+2025=2601 (24,70,74):576+4900=5476 (24,143,145):576+20449=21025 (25,60,65):625+3600=4225 (25,312,313):625+97344=97969 (26,168,170):676+28224=28900 (27,36,45):729+1296=2025 (27,120,123):729+14400=15129 (27,364,365):729+132496=133225 (28,21,35):784+441=1225 (28,45,53):784+2025=2809 (28,96,100):784+9216=10000 (28,195,197):784+38025=38809 (29,420,421):841+176400=177241 (30,16,34):900+256=1156 (30,40,50):900+1600=2500 (30,72,78):900+5184=6084 (30,224,226):900+50176=51076 (31,480,481):961+230400=231361 (32,24,40):1024+576=1600 (32,60,68):1024+3600=4624 (32,126,130):1024+15876=16900 (32,255,257):1024+65025=66049 (33,44,55):1089+1936=3025 (33,56,65):1089+3136=4225 (33,180,183):1089+32400=33489 (34,288,290):1156+82944=84100 (35,12,37):1225+144=1369 (35,84,91):1225+7056=8281 (35,120,125):1225+14400=15625 (36,15,39):1296+225=1521 (36,27,45):1296+729=2025 (36,48,60):1296+2304=3600 (36,77,85):1296+5929=7225 (36,105,111):1296+11025=12321 (36,160,164):1296+25600=26896 (36,323,325):1296+104329=105625 (38,360,362):1444+129600=131044 (39,52,65):1521+2704=4225 (39,80,89):1521+6400=7921 (39,252,255):1521+63504=65025 (40,9,41):1600+81=1681 (40,30,50):1600+900=2500 (40,42,58):1600+1764=3364 (40,75,85):1600+5625=7225 (40,96,104):1600+9216=10816 (40,198,202):1600+39204=40804 (40,399,401):1600+159201=160801 (42,40,58):1764+1600=3364 (42,56,70):1764+3136=4900 (42,144,150):1764+20736=22500 (42,440,442):1764+193600=195364 (44,33,55):1936+1089=3025 (44,117,125):1936+13689=15625 (44,240,244):1936+57600=59536 (44,483,485):1936+233289=235225 (45,24,51):2025+576=2601 (45,28,53):2025+784=2809 (45,60,75):2025+3600=5625 (45,108,117):2025+11664=13689 (45,200,205):2025+40000=42025 (45,336,339):2025+112896=114921 (48,14,50):2304+196=2500 (48,20,52):2304+400=2704 (48,36,60):2304+1296=3600 (48,55,73):2304+3025=5329 (48,64,80):2304+4096=6400 (48,90,102):2304+8100=10404 (48,140,148):2304+19600=21904 (48,189,195):2304+35721=38025 (48,286,290):2304+81796=84100 (49,168,175):2401+28224=30625 (50,120,130):2500+14400=16900 (51,68,85):2601+4624=7225 (51,140,149):2601+19600=22201 (51,432,435):2601+186624=189225 (52,39,65):2704+1521=4225 (52,165,173):2704+27225=29929 (52,336,340):2704+112896=115600 (54,72,90):2916+5184=8100 (54,240,246):2916+57600=60516 (55,48,73):3025+2304=5329 (55,132,143):3025+17424=20449 (55,300,305):3025+90000=93025 (56,33,65):3136+1089=4225 (56,42,70):3136+1764=4900 (56,90,106):3136+8100=11236 (56,105,119):3136+11025=14161 (56,192,200):3136+36864=40000 (56,390,394):3136+152100=155236 (57,76,95):3249+5776=9025 (57,176,185):3249+30976=34225 (60,11,61):3600+121=3721 (60,25,65):3600+625=4225 (60,32,68):3600+1024=4624 (60,45,75):3600+2025=5625 (60,63,87):3600+3969=7569 (60,80,100):3600+6400=10000 (60,91,109):3600+8281=11881 (60,144,156):3600+20736=24336 (60,175,185):3600+30625=34225 (60,221,229):3600+48841=52441 (60,297,303):3600+88209=91809 (60,448,452):3600+200704=204304 (63,16,65):3969+256=4225 (63,60,87):3969+3600=7569 (63,84,105):3969+7056=11025 (63,216,225):3969+46656=50625 (63,280,287):3969+78400=82369 (64,48,80):4096+2304=6400 (64,120,136):4096+14400=18496 (64,252,260):4096+63504=67600 (65,72,97):4225+5184=9409 (65,156,169):4225+24336=28561 (65,420,425):4225+176400=180625 (66,88,110):4356+7744=12100 (66,112,130):4356+12544=16900 (66,360,366):4356+129600=133956 (68,51,85):4624+2601=7225 (68,285,293):4624+81225=85849 (69,92,115):4761+8464=13225 (69,260,269):4761+67600=72361 (70,24,74):4900+576=5476 (70,168,182):4900+28224=33124 (70,240,250):4900+57600=62500 (72,21,75):5184+441=5625 (72,30,78):5184+900=6084 (72,54,90):5184+2916=8100 (72,65,97):5184+4225=9409 (72,96,120):5184+9216=14400 (72,135,153):5184+18225=23409 (72,154,170):5184+23716=28900 (72,210,222):5184+44100=49284 (72,320,328):5184+102400=107584 (72,429,435):5184+184041=189225 (75,40,85):5625+1600=7225 (75,100,125):5625+10000=15625 (75,180,195):5625+32400=38025 (75,308,317):5625+94864=100489 (76,57,95):5776+3249=9025 (76,357,365):5776+127449=133225 (77,36,85):5929+1296=7225 (77,264,275):5929+69696=75625 (77,420,427):5929+176400=182329 (78,104,130):6084+10816=16900 (78,160,178):6084+25600=31684 (80,18,82):6400+324=6724 (80,39,89):6400+1521=7921 (80,60,100):6400+3600=10000 (80,84,116):6400+7056=13456 (80,150,170):6400+22500=28900 (80,192,208):6400+36864=43264 (80,315,325):6400+99225=105625 (80,396,404):6400+156816=163216 (81,108,135):6561+11664=18225 (81,360,369):6561+129600=136161 (84,13,85):7056+169=7225 (84,35,91):7056+1225=8281 (84,63,105):7056+3969=11025 (84,80,116):7056+6400=13456 (84,112,140):7056+12544=19600 (84,135,159):7056+18225=25281 (84,187,205):7056+34969=42025 (84,245,259):7056+60025=67081 (84,288,300):7056+82944=90000 (84,437,445):7056+190969=198025 (85,132,157):7225+17424=24649 (85,204,221):7225+41616=48841 (87,116,145):7569+13456=21025 (87,416,425):7569+173056=180625 (88,66,110):7744+4356=12100 (88,105,137):7744+11025=18769 (88,165,187):7744+27225=34969 (88,234,250):7744+54756=62500 (88,480,488):7744+230400=238144 (90,48,102):8100+2304=10404 (90,56,106):8100+3136=11236 (90,120,150):8100+14400=22500 (90,216,234):8100+46656=54756 (90,400,410):8100+160000=168100 (91,60,109):8281+3600=11881 (91,312,325):8281+97344=105625 (92,69,115):8464+4761=13225 (93,124,155):8649+15376=24025 (93,476,485):8649+226576=235225 (95,168,193):9025+28224=37249 (95,228,247):9025+51984=61009 (96,28,100):9216+784=10000 (96,40,104):9216+1600=10816 (96,72,120):9216+5184=14400 (96,110,146):9216+12100=21316 (96,128,160):9216+16384=25600 (96,180,204):9216+32400=41616 (96,247,265):9216+61009=70225 (96,280,296):9216+78400=87616 (96,378,390):9216+142884=152100 (98,336,350):9604+112896=122500 (99,20,101):9801+400=10201 (99,132,165):9801+17424=27225 (99,168,195):9801+28224=38025 (99,440,451):9801+193600=203401 (100,75,125):10000+5625=15625 (100,105,145):10000+11025=21025 (100,240,260):10000+57600=67600 (102,136,170):10404+18496=28900 (102,280,298):10404+78400=88804 (104,78,130):10816+6084=16900 (104,153,185):10816+23409=34225 (104,195,221):10816+38025=48841 (104,330,346):10816+108900=119716 (105,36,111):11025+1296=12321 (105,56,119):11025+3136=14161 (105,88,137):11025+7744=18769 (105,100,145):11025+10000=21025 (105,140,175):11025+19600=30625 (105,208,233):11025+43264=54289 (105,252,273):11025+63504=74529 (105,360,375):11025+129600=140625 (108,45,117):11664+2025=13689 (108,81,135):11664+6561=18225 (108,144,180):11664+20736=32400 (108,231,255):11664+53361=65025 (108,315,333):11664+99225=110889 (108,480,492):11664+230400=242064 (110,96,146):12100+9216=21316 (110,264,286):12100+69696=81796 (111,148,185):12321+21904=34225 (112,15,113):12544+225=12769 (112,66,130):12544+4356=16900 (112,84,140):12544+7056=19600 (112,180,212):12544+32400=44944 (112,210,238):12544+44100=56644 (112,384,400):12544+147456=160000 (112,441,455):12544+194481=207025 (114,152,190):12996+23104=36100 (114,352,370):12996+123904=136900 (115,252,277):13225+63504=76729 (115,276,299):13225+76176=89401 (116,87,145):13456+7569=21025 (117,44,125):13689+1936=15625 (117,156,195):13689+24336=38025 (117,240,267):13689+57600=71289 (119,120,169):14161+14400=28561 (119,408,425):14161+166464=180625 (120,22,122):14400+484=14884 (120,27,123):14400+729=15129 (120,35,125):14400+1225=15625 (120,50,130):14400+2500=16900 (120,64,136):14400+4096=18496 (120,90,150):14400+8100=22500 (120,119,169):14400+14161=28561 (120,126,174):14400+15876=30276 (120,160,200):14400+25600=40000 (120,182,218):14400+33124=47524 (120,209,241):14400+43681=58081 (120,225,255):14400+50625=65025 (120,288,312):14400+82944=97344 (120,350,370):14400+122500=136900 (120,391,409):14400+152881=167281 (120,442,458):14400+195364=209764 (123,164,205):15129+26896=42025 (124,93,155):15376+8649=24025 (125,300,325):15625+90000=105625 (126,32,130):15876+1024=16900 (126,120,174):15876+14400=30276 (126,168,210):15876+28224=44100 (126,432,450):15876+186624=202500 (128,96,160):16384+9216=25600 (128,240,272):16384+57600=73984 (129,172,215):16641+29584=46225 (130,144,194):16900+20736=37636 (130,312,338):16900+97344=114244 (132,55,143):17424+3025=20449 (132,85,157):17424+7225=24649 (132,99,165):17424+9801=27225 (132,176,220):17424+30976=48400 (132,224,260):17424+50176=67600 (132,351,375):17424+123201=140625 (132,385,407):17424+148225=165649 (132,475,493):17424+225625=243049 (133,156,205):17689+24336=42025 (133,456,475):17689+207936=225625 (135,72,153):18225+5184=23409 (135,84,159):18225+7056=25281 (135,180,225):18225+32400=50625 (135,324,351):18225+104976=123201 (135,352,377):18225+123904=142129 (136,102,170):18496+10404=28900 (136,255,289):18496+65025=83521 (136,273,305):18496+74529=93025 (138,184,230):19044+33856=52900 (140,48,148):19600+2304=21904 (140,51,149):19600+2601=22201 (140,105,175):19600+11025=30625 (140,147,203):19600+21609=41209 (140,171,221):19600+29241=48841 (140,225,265):19600+50625=70225 (140,336,364):19600+112896=132496 (140,480,500):19600+230400=250000 (141,188,235):19881+35344=55225 (143,24,145):20449+576=21025 (144,17,145):20736+289=21025 (144,42,150):20736+1764=22500 (144,60,156):20736+3600=24336 (144,108,180):20736+11664=32400 (144,130,194):20736+16900=37636 (144,165,219):20736+27225=47961 (144,192,240):20736+36864=57600 (144,270,306):20736+72900=93636 (144,308,340):20736+94864=115600 (144,420,444):20736+176400=197136 (145,348,377):21025+121104=142129 (145,408,433):21025+166464=187489 (147,140,203):21609+19600=41209 (147,196,245):21609+38416=60025 (148,111,185):21904+12321=34225 (150,80,170):22500+6400=28900 (150,200,250):22500+40000=62500 (150,360,390):22500+129600=152100 (152,114,190):23104+12996=36100 (152,285,323):23104+81225=104329 (152,345,377):23104+119025=142129 (153,104,185):23409+10816=34225 (153,204,255):23409+41616=65025 (153,420,447):23409+176400=199809 (154,72,170):23716+5184=28900 (155,372,403):24025+138384=162409 (155,468,493):24025+219024=243049 (156,65,169):24336+4225=28561 (156,117,195):24336+13689=38025 (156,133,205):24336+17689=42025 (156,208,260):24336+43264=67600 (156,320,356):24336+102400=126736 (156,455,481):24336+207025=231361 (159,212,265):25281+44944=70225 (160,36,164):25600+1296=26896 (160,78,178):25600+6084=31684 (160,120,200):25600+14400=40000 (160,168,232):25600+28224=53824 (160,231,281):25600+53361=78961 (160,300,340):25600+90000=115600 (160,384,416):25600+147456=173056 (161,240,289):25921+57600=83521 (162,216,270):26244+46656=72900 (164,123,205):26896+15129=42025 (165,52,173):27225+2704=29929 (165,88,187):27225+7744=34969 (165,144,219):27225+20736=47961 (165,220,275):27225+48400=75625 (165,280,325):27225+78400=105625 (165,396,429):27225+156816=184041 (168,26,170):28224+676=28900 (168,49,175):28224+2401=30625 (168,70,182):28224+4900=33124 (168,95,193):28224+9025=37249 (168,99,195):28224+9801=38025 (168,126,210):28224+15876=44100 (168,160,232):28224+25600=53824 (168,224,280):28224+50176=78400 (168,270,318):28224+72900=101124 (168,315,357):28224+99225=127449 (168,374,410):28224+139876=168100 (168,425,457):28224+180625=208849 (170,264,314):28900+69696=98596 (170,408,442):28900+166464=195364 (171,140,221):29241+19600=48841 (171,228,285):29241+51984=81225 (172,129,215):29584+16641=46225 (174,232,290):30276+53824=84100 (175,60,185):30625+3600=34225 (175,288,337):30625+82944=113569 (175,420,455):30625+176400=207025 (176,57,185):30976+3249=34225 (176,132,220):30976+17424=48400 (176,210,274):30976+44100=75076 (176,330,374):30976+108900=139876 (176,468,500):30976+219024=250000 (177,236,295):31329+55696=87025 (180,19,181):32400+361=32761 (180,33,183):32400+1089=33489 (180,75,195):32400+5625=38025 (180,96,204):32400+9216=41616 (180,112,212):32400+12544=44944 (180,135,225):32400+18225=50625 (180,189,261):32400+35721=68121 (180,240,300):32400+57600=90000 (180,273,327):32400+74529=106929 (180,299,349):32400+89401=121801 (180,385,425):32400+148225=180625 (180,432,468):32400+186624=219024 (182,120,218):33124+14400=47524 (183,244,305):33489+59536=93025 (184,138,230):33856+19044=52900 (184,345,391):33856+119025=152881 (185,444,481):34225+197136=231361 (186,248,310):34596+61504=96100 (187,84,205):34969+7056=42025 (188,141,235):35344+19881=55225 (189,48,195):35721+2304=38025 (189,180,261):35721+32400=68121 (189,252,315):35721+63504=99225 (189,340,389):35721+115600=151321 (190,336,386):36100+112896=148996 (190,456,494):36100+207936=244036 (192,56,200):36864+3136=40000 (192,80,208):36864+6400=43264 (192,144,240):36864+20736=57600 (192,220,292):36864+48400=85264 (192,256,320):36864+65536=102400 (192,360,408):36864+129600=166464 (195,28,197):38025+784=38809 (195,104,221):38025+10816=48841 (195,216,291):38025+46656=84681 (195,260,325):38025+67600=105625 (195,400,445):38025+160000=198025 (196,147,245):38416+21609=60025 (196,315,371):38416+99225=137641 (198,40,202):39204+1600=40804 (198,264,330):39204+69696=108900 (198,336,390):39204+112896=152100 (200,45,205):40000+2025=42025 (200,150,250):40000+22500=62500 (200,210,290):40000+44100=84100 (200,375,425):40000+140625=180625 (201,268,335):40401+71824=112225 (203,396,445):41209+156816=198025 (204,85,221):41616+7225=48841 (204,153,255):41616+23409=65025 (204,253,325):41616+64009=105625 (204,272,340):41616+73984=115600 (207,224,305):42849+50176=93025 (207,276,345):42849+76176=119025 (208,105,233):43264+11025=54289 (208,156,260):43264+24336=67600 (208,306,370):43264+93636=136900 (208,390,442):43264+152100=195364 (209,120,241):43681+14400=58081 (210,72,222):44100+5184=49284 (210,112,238):44100+12544=56644 (210,176,274):44100+30976=75076 (210,200,290):44100+40000=84100 (210,280,350):44100+78400=122500 (210,416,466):44100+173056=217156 (212,159,265):44944+25281=70225 (213,284,355):45369+80656=126025 (216,63,225):46656+3969=50625 (216,90,234):46656+8100=54756 (216,162,270):46656+26244=72900 (216,195,291):46656+38025=84681 (216,288,360):46656+82944=129600 (216,405,459):46656+164025=210681 (219,292,365):47961+85264=133225 (220,21,221):48400+441=48841 (220,165,275):48400+27225=75625 (220,192,292):48400+36864=85264 (220,231,319):48400+53361=101761 (221,60,229):48841+3600=52441 (222,296,370):49284+87616=136900 (224,30,226):50176+900=51076 (224,132,260):50176+17424=67600 (224,168,280):50176+28224=78400 (224,207,305):50176+42849=93025 (224,360,424):50176+129600=179776 (224,420,476):50176+176400=226576 (225,120,255):50625+14400=65025 (225,140,265):50625+19600=70225 (225,272,353):50625+73984=124609 (225,300,375):50625+90000=140625 (228,95,247):51984+9025=61009 (228,171,285):51984+29241=81225 (228,304,380):51984+92416=144400 (228,325,397):51984+105625=157609 (231,108,255):53361+11664=65025 (231,160,281):53361+25600=78961 (231,220,319):53361+48400=101761 (231,308,385):53361+94864=148225 (231,392,455):53361+153664=207025 (232,174,290):53824+30276=84100 (232,435,493):53824+189225=243049 (234,88,250):54756+7744=62500 (234,312,390):54756+97344=152100 (236,177,295):55696+31329=87025 (237,316,395):56169+99856=156025 (238,240,338):56644+57600=114244 (240,44,244):57600+1936=59536 (240,54,246):57600+2916=60516 (240,70,250):57600+4900=62500 (240,100,260):57600+10000=67600 (240,117,267):57600+13689=71289 (240,128,272):57600+16384=73984 (240,161,289):57600+25921=83521 (240,180,300):57600+32400=90000 (240,238,338):57600+56644=114244 (240,252,348):57600+63504=121104 (240,275,365):57600+75625=133225 (240,320,400):57600+102400=160000 (240,364,436):57600+132496=190096 (240,418,482):57600+174724=232324 (243,324,405):59049+104976=164025 (244,183,305):59536+33489=93025 (245,84,259):60025+7056=67081 (246,328,410):60516+107584=168100 (247,96,265):61009+9216=70225 (248,186,310):61504+34596=96100 (249,332,415):62001+110224=172225 (252,39,255):63504+1521=65025 (252,64,260):63504+4096=67600 (252,105,273):63504+11025=74529 (252,115,277):63504+13225=76729 (252,189,315):63504+35721=99225 (252,240,348):63504+57600=121104 (252,275,373):63504+75625=139129 (252,336,420):63504+112896=176400 (252,405,477):63504+164025=227529 (253,204,325):64009+41616=105625 (255,32,257):65025+1024=66049 (255,136,289):65025+18496=83521 (255,340,425):65025+115600=180625 (255,396,471):65025+156816=221841 (256,192,320):65536+36864=102400 (258,344,430):66564+118336=184900 (260,69,269):67600+4761=72361 (260,195,325):67600+38025=105625 (260,273,377):67600+74529=142129 (260,288,388):67600+82944=150544 (261,348,435):68121+121104=189225 (261,380,461):68121+144400=212521 (264,23,265):69696+529=70225 (264,77,275):69696+5929=75625 (264,110,286):69696+12100=81796 (264,170,314):69696+28900=98596 (264,198,330):69696+39204=108900 (264,315,411):69696+99225=168921 (264,352,440):69696+123904=193600 (266,312,410):70756+97344=168100 (267,356,445):71289+126736=198025 (268,201,335):71824+40401=112225 (270,144,306):72900+20736=93636 (270,168,318):72900+28224=101124 (270,360,450):72900+129600=202500 (272,204,340):73984+41616=115600 (272,225,353):73984+50625=124609 (273,136,305):74529+18496=93025 (273,180,327):74529+32400=106929 (273,260,377):74529+67600=142129 (273,364,455):74529+132496=207025 (275,240,365):75625+57600=133225 (275,252,373):75625+63504=139129 (276,115,299):76176+13225=89401 (276,207,345):76176+42849=119025 (276,368,460):76176+135424=211600 (279,372,465):77841+138384=216225 (280,63,287):78400+3969=82369 (280,96,296):78400+9216=87616 (280,102,298):78400+10404=88804 (280,165,325):78400+27225=105625 (280,210,350):78400+44100=122500 (280,294,406):78400+86436=164836 (280,342,442):78400+116964=195364 (280,351,449):78400+123201=201601 (282,376,470):79524+141376=220900 (284,213,355):80656+45369=126025 (285,68,293):81225+4624=85849 (285,152,323):81225+23104=104329 (285,380,475):81225+144400=225625 (286,48,290):81796+2304=84100 (288,34,290):82944+1156=84100 (288,84,300):82944+7056=90000 (288,120,312):82944+14400=97344 (288,175,337):82944+30625=113569 (288,216,360):82944+46656=129600 (288,260,388):82944+67600=150544 (288,330,438):82944+108900=191844 (288,384,480):82944+147456=230400 (291,388,485):84681+150544=235225 (292,219,365):85264+47961=133225 (294,280,406):86436+78400=164836 (294,392,490):86436+153664=240100 (296,222,370):87616+49284=136900 (297,60,303):88209+3600=91809 (297,304,425):88209+92416=180625 (297,396,495):88209+156816=245025 (299,180,349):89401+32400=121801 (300,55,305):90000+3025=93025 (300,125,325):90000+15625=105625 (300,160,340):90000+25600=115600 (300,225,375):90000+50625=140625 (300,315,435):90000+99225=189225 (300,400,500):90000+160000=250000 (304,228,380):92416+51984=144400 (304,297,425):92416+88209=180625 (306,208,370):93636+43264=136900 (308,75,317):94864+5625=100489 (308,144,340):94864+20736=115600 (308,231,385):94864+53361=148225 (312,25,313):97344+625=97969 (312,91,325):97344+8281=105625 (312,130,338):97344+16900=114244 (312,234,390):97344+54756=152100 (312,266,410):97344+70756=168100 (315,80,325):99225+6400=105625 (315,108,333):99225+11664=110889 (315,168,357):99225+28224=127449 (315,196,371):99225+38416=137641 (315,264,411):99225+69696=168921 (315,300,435):99225+90000=189225 (316,237,395):99856+56169=156025 (319,360,481):101761+129600=231361 (320,72,328):102400+5184=107584 (320,156,356):102400+24336=126736 (320,240,400):102400+57600=160000 (320,336,464):102400+112896=215296 (323,36,325):104329+1296=105625 (324,135,351):104976+18225=123201 (324,243,405):104976+59049=164025 (325,228,397):105625+51984=157609 (325,360,485):105625+129600=235225 (328,246,410):107584+60516=168100 (330,104,346):108900+10816=119716 (330,176,374):108900+30976=139876 (330,288,438):108900+82944=191844 (332,249,415):110224+62001=172225 (336,45,339):112896+2025=114921 (336,52,340):112896+2704=115600 (336,98,350):112896+9604=122500 (336,140,364):112896+19600=132496 (336,190,386):112896+36100=148996 (336,198,390):112896+39204=152100 (336,252,420):112896+63504=176400 (336,320,464):112896+102400=215296 (340,189,389):115600+35721=151321 (340,255,425):115600+65025=180625 (340,357,493):115600+127449=243049 (342,280,442):116964+78400=195364 (344,258,430):118336+66564=184900 (345,152,377):119025+23104=142129 (345,184,391):119025+33856=152881 (348,145,377):121104+21025=142129 (348,261,435):121104+68121=189225 (350,120,370):122500+14400=136900 (351,132,375):123201+17424=140625 (351,280,449):123201+78400=201601 (352,114,370):123904+12996=136900 (352,135,377):123904+18225=142129 (352,264,440):123904+69696=193600 (356,267,445):126736+71289=198025 (357,76,365):127449+5776=133225 (357,340,493):127449+115600=243049 (360,38,362):129600+1444=131044 (360,66,366):129600+4356=133956 (360,81,369):129600+6561=136161 (360,105,375):129600+11025=140625 (360,150,390):129600+22500=152100 (360,192,408):129600+36864=166464 (360,224,424):129600+50176=179776 (360,270,450):129600+72900=202500 (360,319,481):129600+101761=231361 (360,325,485):129600+105625=235225 (364,27,365):132496+729=133225 (364,240,436):132496+57600=190096 (364,273,455):132496+74529=207025 (368,276,460):135424+76176=211600 (372,155,403):138384+24025=162409 (372,279,465):138384+77841=216225 (374,168,410):139876+28224=168100 (375,200,425):140625+40000=180625 (376,282,470):141376+79524=220900 (378,96,390):142884+9216=152100 (380,261,461):144400+68121=212521 (380,285,475):144400+81225=225625 (384,112,400):147456+12544=160000 (384,160,416):147456+25600=173056 (384,288,480):147456+82944=230400 (385,132,407):148225+17424=165649 (385,180,425):148225+32400=180625 (388,291,485):150544+84681=235225 (390,56,394):152100+3136=155236 (390,208,442):152100+43264=195364 (391,120,409):152881+14400=167281 (392,231,455):153664+53361=207025 (392,294,490):153664+86436=240100 (396,80,404):156816+6400=163216 (396,165,429):156816+27225=184041 (396,203,445):156816+41209=198025 (396,255,471):156816+65025=221841 (396,297,495):156816+88209=245025 (399,40,401):159201+1600=160801 (400,90,410):160000+8100=168100 (400,195,445):160000+38025=198025 (400,300,500):160000+90000=250000 (405,216,459):164025+46656=210681 (405,252,477):164025+63504=227529 (408,119,425):166464+14161=180625 (408,145,433):166464+21025=187489 (408,170,442):166464+28900=195364 (416,87,425):173056+7569=180625 (416,210,466):173056+44100=217156 (418,240,482):174724+57600=232324 (420,29,421):176400+841=177241 (420,65,425):176400+4225=180625 (420,77,427):176400+5929=182329 (420,144,444):176400+20736=197136 (420,153,447):176400+23409=199809 (420,175,455):176400+30625=207025 (420,224,476):176400+50176=226576 (425,168,457):180625+28224=208849 (429,72,435):184041+5184=189225 (432,51,435):186624+2601=189225 (432,126,450):186624+15876=202500 (432,180,468):186624+32400=219024 (435,232,493):189225+53824=243049 (437,84,445):190969+7056=198025 (440,42,442):193600+1764=195364 (440,99,451):193600+9801=203401 (441,112,455):194481+12544=207025 (442,120,458):195364+14400=209764 (444,185,481):197136+34225=231361 (448,60,452):200704+3600=204304 (455,156,481):207025+24336=231361 (456,133,475):207936+17689=225625 (456,190,494):207936+36100=244036 (468,155,493):219024+24025=243049 (468,176,500):219024+30976=250000 (475,132,493):225625+17424=243049 (476,93,485):226576+8649=235225 (480,31,481):230400+961=231361 (480,88,488):230400+7744=238144 (480,108,492):230400+11664=242064 (480,140,500):230400+19600=250000 (483,44,485):233289+1936=235225