SOLUTION: if p-n^2=x and (n+1)^2-p=y then,prove that p-xy is a perfect square.

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Question 479507: if p-n^2=x and (n+1)^2-p=y then,prove that p-xy is a perfect square.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
p - xy
=p+-+%28p-n%5E2%29%28%28n%2B1%29%5E2+-+p%29
=p+-+%28p%28n%2B1%29%5E2+-+p%5E2+-+n%5E2%28n%2B1%29%5E2+%2B+n%5E2p%29
=p+-+p%28n%2B1%29%5E2+%2B+p%5E2+%2B+n%5E2%28n%2B1%29%5E2+-+n%5E2p
=p+-+p%28n%5E2+%2B+2n+%2B+1%29+%2B+p%5E2+%2B+n%5E2%28n%2B1%29%5E2+-+n%5E2p
=p+-+pn%5E2+-+2pn+-+p+%2B+p%5E2+%2B+n%5E2%28n%2B1%29%5E2+-+n%5E2p
=-+2pn%5E2+-+2pn+%2B+p%5E2+%2B+n%5E2%28n%2B1%29%5E2
=-+2pn%5E2+-n%5E2++%2B+p%5E2+-+2pn+%2B+n%5E2+%2B++n%5E2%28n%2B1%29%5E2
=-+2pn%5E2+-n%5E2++%2B%28p-n%29%5E2+%2B++n%5E2%28n%2B1%29%5E2
= -n%5E2%281+%2B+2p%29+%2B+%28p-n%29%5E2+%2B+n%5E2%28n%2B1%29%5E2
=n%5E2%28%28n%2B1%29%5E2+-+%281%2B2p%29%29+%2B+%28p-n%29%5E2
= n%5E2%28n%5E2+%2B+2n+-+2p%29+%2B+%28p-n%29%5E2
= n%5E4+-+2n%5E2%28p-n%29+%2B+%28p-n%29%5E2
=%28n%5E2+-+%28p-n%29%29%5E2
=%28n%5E2+%2B+n+-+p%29%5E2
and the proof is complete...