Leta=75andb=27. (a) Use the Euclidean Algorithm (or the modified Euclidean Algorithm) to find gcd(a, b).

3) Use the Euclidean algorithm to compute gcd(428, 484).

Use the Euclidean algorithm to find the greatest common divisor of theFibonacci numbers u12 = 144 and u11 = 89.

Someone used the Euclidean Algorithm to compute gcd(44,140) and found the following. Use this to write the gcd as a linear combination of 44 and 140. Show work.  140 = 3(44) + 8 44 = 5(8) + 4 8 = 2(4) + 0

(a) Use the Euclidean algorithm to find gcd(131,326). (b) Use the above to find a solution to 131x+326y=gcd(131,326) (c) Does 131 have an inverse modulo 326? If so, find a value in {0,1,2,3,…,325} that is an inverse. If not, explain why not?

a) (123mod 19 ▪ 342 mod 19) mod 19 b) (12² mod 17)³ mod 13 2) (10 pts) Prove or disprove that for all integers a, b, and c, if alb and b/c then alc.