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Math Help - Equation with prime numbers

  1. #1
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    Equation with prime numbers

    We should find all the (p, q, n) triples, where p and q are prime numbers, n is a natural number and the following equation is true:
    n^2=p^2+q^2+p^2*q^2
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    Quote Originally Posted by doug View Post
    We should find all the (p, q, n) triples, where p and q are prime numbers, n is a natural number and the following equation is true:
    n^2=p^2+q^2+p^2*q^2
    Two obvious solutions are (p,q,n) = (2,3,7) and (3,2,7). To proceed, possibly use that any odd number squared is congruent to 1 mod 8, and that there is only one even prime. (Haven't worked it out beyond that.)
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  3. #3
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    Proceeding, using the above information you can show that one of p,q is 2 and the other is odd, then if you consider mod 3 you will see the above solutions are the only possible.
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