1. Prove the following statements: a) For all n E Z, either 112 E 0 (mod 4) or n2 E 1 (mod 4). b) lfn E N is odd, then 11,2 E 1 (mod 8). 2. Use Fermat's Little Theorem to show that 51839203 E 12 (mod 13). (Note: You must use Fermat's Little Theorem for your answer to be considered correct.) 3. a) Use the Euclidean Algorithm to calculate god(11245,8920). b) Use your answer in (a) to determine whether 8920 has a multiplicative inverse as an element of Z11245. Explain how you know. c) Reverse the Euclidean Algorithm to express your answer in (a) as a linear combination of 11245 and 8920 (i.e. Find x and y that solves the expression god (11245, 8920) = 8970x + 11748y.)