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primes of the form (a-1)*(a^(p*q)-1)/(a^p-1)/(a^q-1)

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  • Edwin Clark
    Is there a name for and/or have primes of the form (a-1)*(a^(p*q)-1)/(a^p-1)/(a^q-1) been studied? Here p and q are primes and a is any positive integer. Many
    Message 1 of 1 , Mar 6, 2004
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      Is there a name for and/or have primes of the form

      (a-1)*(a^(p*q)-1)/(a^p-1)/(a^q-1)

      been studied?

      Here p and q are primes and a is any positive integer. Many of these
      numbers are prime. Especially nice is the case a = 2 when we have

      (2^(p*q)-1)/( (2^p-1)*(2^q-1))

      Note that (x-1)*(x^(p*q)-1)/(x^p-1)/(x^q-1) is the pq-th cyclotomic
      polynomial. In particular, it is a polynomial with integer coefficients.

      Except for the case where p or q is 2, these primes don't appear to be in
      the OEIS.

      --Edwin Clark
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