How would I go about proving that 8^n - 3^n (n >= 1) is divisible by 5 using mathematical induction? I tried this but I do not think it is right:(adsbygoogle = window.adsbygoogle || []).push({});

First, prove that 8^1 - 3^1 is divisible by 5. 8^1 - 3^1 = 5, which is divisible by 5.

Second, prove that 8^(k+1) - 3^(k+1) is divisible by 5 if k = n. Notice that 8^(k+1) - 3^(k+1) =

8*(8^k) - 3^k(3). Based on the induction hypothesis, we already know that 8^k - 3^k is divisible by 5. So we end up with 24*(8^k - 3^k), which is always divisible by 5 because the term inside the parenthesis is already divisible by 5. Multiplying that by any number will not change the fact that it is divisible by 5.

Am I right here? Thanks.

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# Proof by Induction

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