Let n Z with n 1 a) If n 2k where k is an odd integer, prove that k3 k (mod n) b) If n 4k for some k Z , prove that (2k)2 0 (mod ft) c) Prove that 10(modn), otherwise with or n even old (mod n otherwise

Question: Let n Z+ with n > 1. a) If n = 2k where k is an odd integer, prove that k3 =k (mod n).

Let n ˆˆ Z+ with n > 1.
a) If n = 2k where k is an odd integer, prove that
k3 =k (mod n).
b) If n = 4k for some k ˆˆ Z+, prove that
(2k)2 = 0 (mod ft).
c) Prove that

10(modn), otherwise. with or n even old. (mod n otherwise.

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