Prove the following if x is of the form x nk 1 for some
Let n > 1 be a fixed natural number.
(a) Prove the following: if x is of the form x = nk + 1 for some natural number k, then x^2 ≡ 1 mod n.
(b) Find a y ∈ N and an n ∈ N such that y (not congruent) 1 mod n and y^2 ≡ 1 mod n.
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