2.7^n +3.5^n -5 is divisible by 24.
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Prove by induction that for all natural numbers n, n3 − n is divisible by 3. 3.2 (5.2 of [IMR]) Prove by induction that n3 ≤ 2n for all integers n with n ≥ 10. 3.3 Prove by induction on n that 13 divides 24n+2 +3n+2 for all natural numbers n.
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