How many pairs of distinct positive integers $\displaystyle a, b: (b > a)$ exist such that $\displaystyle (a^2 + 1)(b^2 + 1)$ is a square?
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Originally Posted by icemanfan How many pairs of distinct positive integers $\displaystyle a, b: (b > a)$ exist such that $\displaystyle (a^2 + 1)(b^2 + 1)$ is a square? start with this identity: $\displaystyle (a^2+1)(b^2+1)=(ab \pm 1)^2+(a \mp b)^2.$
Last edited by NonCommAlg; Feb 15th 2010 at 12:41 AM.
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