tP" 99951539" IO 11, 12. 13. 14, MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Assignment 7 Mathematics 2320 Winter 2017 Due: March 17 , 2017 . SHOW ALL WORK . Find q and r, with O S r g lbl, such that a : qb + r for (a) a : 400, b: -17 (b) a = -312,b = -64 Find the god(a, b) for (a) a = 504, b: 60 140, b = 675 Determine whether 2491 and 1134 are relatively prime. For a : 450, b : 140 find m and n such that ged(a,b) : ma + nb: Find integers m and n such that 7m + 1911 = 13 Show that no integers z, y satisfy 1961 + 260]; = 14. Find the lcm(a,b) for a = 450, b = 140 Find all integers a % 3 for which (a 7 3)I(a3 7 3) Determine for which natural number n the number n2 + 1 is divisible by n + 1. Prove that, for integers a and b, ged(a., a + b) = ged(a, b). Show that if a and b are relatively prime and ale and his, then able If f : Z30 H Zgg is defined by f([a]) = [711], then show that f is Well defined, one-to-one and onto and find f'l. Find a number 'V' With 0 g r < 39 such that (a) 42,162 E Mmod 39) (b) -3142 E r(rn0d 39) Solve each of the following eongruenees: (a) 71 E 6(mod 23) (b) 251 E 5 (mod 92)