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Homework Help: Help with proof

  1. Apr 7, 2006 #1
    I got stuck on one part of this proof. I'm trying to show that
    (2(p1)(p2).....(pn))^4 + 1 is divisible by an odd prime q. Can anyone help with some suggestions?
  2. jcsd
  3. Apr 7, 2006 #2
    I take it you left out a bunch of hypotheses, such that the p_i are integer and non-zero. The result then follows immediately from the fundamental theorem of arithmetic.
  4. Apr 7, 2006 #3
    p_i are primes and q is an odd prime different from the p_i's
  5. Apr 7, 2006 #4


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    The point of Muzza's statement about the "fundamental theorem of arithmetic" is that every number is divisible by a prime number! All you need to do is show that (2(p1)(p2).....(pn))^4 + 1 is not divisible by any of the pi (what would the remainder be?) and that it is not divisible by 2.
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