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Is the following theorem well known?

Theorem Odd positive integer N is a prime number if and only if there is no non-trivial solution for Diophantine equation

$x^2−y^2=N$

(trivial solution: $x=(N+1)/2; y=(N−1)/2)$

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I believe this is true and quite clear. Say $p$ is odd and $p = ab$, and $a \geq b > 1$. Solve for $x+y = a$, $x-y = b$. This is possible over the integers since $a$ and $b$ are odd.

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  • $\begingroup$ Example. N=47. There is only trivial solution x=24; y=23. N- is prime. N=81 There is non- trivial solution x=15; y=12. N- is not prime $\endgroup$ – Boris Sklyar Nov 12 '15 at 14:21
  • $\begingroup$ @BorisSklyar I'm aware. What are you asking? $\endgroup$ – djechlin Nov 12 '15 at 14:43
  • $\begingroup$ I am asking: Is proposed theorem correct and is it well known? $\endgroup$ – Boris Sklyar Nov 12 '15 at 14:48
  • $\begingroup$ @BorisSklyar "I believe this is true and quite clear." $\endgroup$ – djechlin Nov 12 '15 at 15:09

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