Number theory problems for PRMO

By Mathfreaks

1)How do you prove that $2 a^{4} + 2 b^{4} + 2 c^{4}$ is a perfect square where $a + b + c = 0$ and all are integers?

2)Detennine all non-negative integral pairs (x,y) for which

(xy-7)^2=x^2+y^2

3)prove that

4 l^{2} = m n

l m x^{2} + m n x + l n

is a perfect square

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