Let
![a, b, c](/media/m/9/e/9/9e9dfe78930065fbe5a777e9b07c27c4.png)
be integers and
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
an odd prime number. Prove that if
![f(x) = ax^2 + bx + c](/media/m/d/7/9/d79d71a550ac351d0ed7d5901460a535.png)
is a perfect square for
![2p - 1](/media/m/f/2/a/f2a896d1a928564a8b9242380851d7b8.png)
consecutive integer values of
![x,](/media/m/a/9/6/a96327826d8ff11119b89ba22bc1e70a.png)
then
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
divides
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Let $a, b, c$ be integers and $p$ an odd prime number. Prove that if $f(x) = ax^2 + bx + c$ is a perfect square for $2p - 1$ consecutive integer values of $x,$ then $p$ divides $b^2 - 4ac.$