Question

1. Prove that 5^2n+1 + 2^2n+1 is divisible by 7 for all n ≥ 0.
2. Prove that a^2 − 1 is divisible by 8 for all odd integers a.
3. Prove that a^4 − 1 is divisible by 16 for all odd integers a.
4. Prove that a^2 n − 1 is divisible by 4 × 2 n for all odd integers a, and for all integers n.
5. Prove that n^3 + 2n is divisible by 3 for all integers n.
6. Prove that 17n^3 + 103n is divisible by 6 for all integers n.
7. Prove that 2^n + 1 is divisible by 3 for all odd integers n.

Answer 1

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