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Is it true that the product of $n>1$ consecutive integers is never a $k$-th power of another integer for any $k \geq 2$?

I can see this is true in certain cases. For instance if the product ends on a prime, But how would one prove this in general?

Thanks for any help or suggestions.

1 Answers 1

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Yes, this is true. This was proven by Erdős and Selfridge in this paper.

  • 0
    Well, that wasn't the short proof I was expecting.2011-04-16
  • 4
    @Carl, whatever made you expect a short proof?2011-04-16
  • 1
    @Gerry; Because I'm quite stupid.2011-04-17
  • 2
    @Carl, cheer up, we're all quite stupid - that's why we're here.2011-04-18
  • 0
    @Gerry; Actually, the miserable people I know are all quite smart.2011-04-18