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Let $z$ be a positive integer. How should one compute all $z$ such that $5^z-1$ can be written as the product of an even number of consecutive positive integers?

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    Brian, I see that this is your first question. So I wanted to let you know a few things about MathSE. We like to know the sources of questions. We also like to know what you've tried on a problem. These sort of pleasantries usually result in more and better answers. Finally, I should add that posting questions in the imperative (i.e. Compute all such...) is considered rude by some of the members, so I advise you to change that wording.2011-08-28
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    @mixedmath: are you sure this is not $5^z - 1$?2011-08-28
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    Note that 6 or more consecutive positive integers must include a multiple of 5, and so there can be no solutions with 6 or more positive integers. Combine that with Byron Schmuland's solution of the case of 4 consecutive positive integers and user14044's disposition of the case of 2 consecutive positive integers, and you are done.2011-08-28

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