Assignment:
Q1) Suppose n ∈ Z.
(a) Prove that if n ≡ 2 (mod 4), then n is not a difference of two squares.
(b) Prove that if n is not congruent to 2 (mod 4), then n is a difference of two squares.
Q2) Let n = 3(t-1). Show that 2n is congruent to -1 (mod 3t).
Q3) Let p be an odd prime, and n = 2p. Show that a(n-1) is congruent to a (mod n) for any integer a.
Provide complete and step by step solution for the question and show calculations and use formulas.