An exercise in number theory?

I seem to have come across a curious little question whilst wondering if a generalised quadrangle can have a product structure, and it comes down to a question about numbers. I’ve been unable to figure it out, but I’m sure it’s not hard. Can somebody prove the following?

Let s be an integer greater than 2 and suppose (s+1)(s^2+1) is a nontrivial power of a positive integer. Then s = 7.

 

 

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