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Re: [PrimeNumbers] obvious???

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  • Joshua Zucker
    ... Yes. 2^whatever is even, 3^whatever is odd, so 2^x + 3^y - 1 is even. 2^even = 1 (mod 3), 3^whatever = 0 (mod 3), so 2^even + 3^whatever - 1 is divisible
    Message 1 of 3 , Jan 16, 2007
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      On 1/16/07, leavemsg1 <leavemsg1@...> wrote:
      > Is it entirely obvious that 2^(p-1)+3^(p-2) -1 is always divisible by 2
      > and 3 where p is prime???

      Yes.

      2^whatever is even, 3^whatever is odd, so 2^x + 3^y - 1 is even.

      2^even = 1 (mod 3), 3^whatever = 0 (mod 3), so
      2^even + 3^whatever - 1 is divisible by 3.

      So if p is odd (not necessarily prime, and not 2), then the
      divisibility will happen as you have said.

      --Joshua ucker
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