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Hi there all, I have a question that I sincerely don't know how to solve and so would like to discuss it with you guys for any possible solutions.

Here's the problem:

I need to prove by induction that n

I start by proving P(1) is true, that is, 1

Next, I assume that P(n－1) is true and use this assumption to prove that P(n) is true.

I wrote:

P(n－1) => (n－1)

(n－1)*[(n－1)

Then I had no idea what to do next. I know at the end I have to prove that P(n－1) is a multiple of 30, but how should I prove that by induction? Can anyone help me with this please!

Here's the problem:

I need to prove by induction that n

^{5}－n is divisible by 30.I start by proving P(1) is true, that is, 1

^{5}－1=0=30k where k=0. This shows that P(1) is divisible by 30 so it's true.Next, I assume that P(n－1) is true and use this assumption to prove that P(n) is true.

I wrote:

P(n－1) => (n－1)

^{5}－(n－1) = 30k(n－1)*[(n－1)

^{5}－1] = 30kThen I had no idea what to do next. I know at the end I have to prove that P(n－1) is a multiple of 30, but how should I prove that by induction? Can anyone help me with this please!

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