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Is the following statement true; "For any odd prime number $p$ , any set of $p-1$ consecutive integers can not be partitioned into two subsets such that the elements of the two sets have equal product." ( I think I read somewhere that Erdos proved it but now I can not remember where I read so , I can only prove the statement for prime of the form $ 4k+3$ , any complete solution or link would be very helpful)

Souvik Dey
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    Isn't it true more generally that the product of (any number of) consecutive integers can't be a square? can't be a $k$th power for any $k\ge2$? – Gerry Myerson Aug 13 '13 at 12:05
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    No, but I've given you a link. See also http://math.stackexchange.com/questions/33338/product-of-consecutive-integers-is-not-a-power – Gerry Myerson Aug 13 '13 at 12:11

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Erdos and Selfridge, The product of consecutive integers is never a power, Illinois J Math 19 (1975) 292-301.

Glorfindel
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Gerry Myerson
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