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How can I prove the following, where $p$ is a prime and $x$ a positive integer?

$\dfrac{(2px)!}{((px)!)^2}\equiv\dfrac{(2x)!}{((x)!)^2}\pmod{p^2}$

I'm not sure if it is actually true, but I tested for small numbers and it checked.

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    Perhaps someone should write up these comments as an answer. Ricbit, it's OK if you do it, now that you have an answer to your question.2012-07-30

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