Question: 1. (a) Use the Euclidean Algorithm to find the inverse of 41 in Z131. (b) Use (a) to solve the equation 41x + 1 =

1. (a) Use the Euclidean Algorithm to find the inverse of 41 in Z131. (b) Use (a) to solve the equation 41x + 1 = 10 in Z131. 2. Using Fermat's Little Theorem, find the remainder when 31403 is divided by 101. 3. (a) Determine the squares modulo 4. That is, find integers a such that x2 = a (mod 4) for some integer x. (b) Prove that if a = 1 (mod 2) then a2 = 1 (mod 4)

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