# Another squares problem

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• February 11th 2010, 03:30 PM
icemanfan
Another squares problem
How many pairs of distinct positive integers $a, b: (b > a)$ exist such that $(a^2 + 1)(b^2 + 1)$ is a square?
• February 15th 2010, 12:30 AM
NonCommAlg
Quote:

Originally Posted by icemanfan
How many pairs of distinct positive integers $a, b: (b > a)$ exist such that $(a^2 + 1)(b^2 + 1)$ is a square?

start with this identity: $(a^2+1)(b^2+1)=(ab \pm 1)^2+(a \mp b)^2.$ (Wink)