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  3. prove that for every n ? n: a) (10^n + 3 * 4^(n+2)

Prove that for every n ? N: a) (10^n + 3 * 4^(n+2)) ? 4 mod...

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Question

Advance Math

Prove that for every n ? N:

a) (10^n + 3 * 4^(n+2)) ? 4 mod 19, [note that 4^3 ? 1 mod9]

b) 24 | (2*7^(n) + 3*5^(n) - 5),

c) 14 | (3^(4n+2) + 5^(2n+1) [Note that 3^(4n+2) + 5^(2n+1) =9^(2n)*9 + 5^(2n)*5 ? (-5)^(2n) * 9 + 5^(2n) *5 ? 0 mod 14]

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