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Possible Duplicate:
On the equation $(a^2+1)(b^2+1)=c^2+1$

I came across a problem: What is relation between $b$ and $c$ such that $b^2 + c^2 + b^2 c^2$ is a perfect square?

After trying few cases, I got following relations:

  • $c = 2b^2$
  • $c = b+1$

But it still doesn't cover all cases e.g. $(1,12),(2,21),(2,55),(3,80),(8,30)$ etc. How do I find general relation ?

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    This is $(b^2+1)(c^2+1)=d^2+1$. I think it's been asked here before - I'll be back if I find it before someone else does.2012-09-16

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