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25338Re: [PrimeNumbers] Yet another factoring puzzle

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  • Kevin Acres
    Aug 24, 2013
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      [snip]
      >
      > Practice: Here are some exercises where wetware helps. I
      > have tried to grade them, starting with easy pencil-and-
      > paper mathematics and ending with something approaching
      > state-of-the-art factorization.
      >
      > Definition: Let F(n) = ((5^n-9)/4)^2-5 for integer n > 0.
      >
      > Exercise 1: For even n > 2, prove that F(n) is composite.
      >
      > Exercise 2: For odd n > 1, prove that F(n)/4 is composite.

      I did work out an algorithm to derive one divisor of F(n)/4 for odd n, but
      that's probably a long way from proving it composite.

      [snip]


      Regards,

      Kevin.
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