Relation between b and c such that $ b^2 + c^2 + b^2 c^2$ is a perfect square

Asked Sep 16 '12 at 05:50

Active Sep 16 '12 at 06:58

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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:

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 ?

edited Apr 13 '17 at 12:21

Community

asked Sep 16 '12 at 05:50

Shashwat Kumar

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. – Gerry Myerson Sep 16 '12 at 06:10

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