6. Calculate the following problems (18 pts). a. 7+1334= b. 51119= c. 17+131= d. 47+130= e. 55111= f. 55110=0 7. Express gcd(990,502)=2 as a linear combination of 990 and 502 by working backwards through the steps of the Euclidean algorithm (10 pts). [Hint: refer to Example 17 in the textbook Section 4.3.8] 8. Show that if ab(modm) and cd(modm), where a,b,c,d, and m are integers with m 2 , then acbd(modm)(10pts). 9. Let a and b be positive integers. Then ab=gcd(a,b)lcm(a,b). a. Please prove it and show the intermediate steps (15 pts). [Hint: Use the prime factorizations of a and b and the formulae for gcd(a,b) and lcm(a,b) in terms of these factorizations. You also can use any other methods.] b. Verify that gcd(744,558)lcm(744,558)=744558(5pts)