7

[Buck Mulligan]

Can you prove that 7 is the only number >1 which increased by one is
the double of a square, and whose square, increased by one is also the
double of a square.

Or in other words, prove that the only solution x>1 of x+1=2*y^2 and
x^2 +1 = 2*z^2 is x = 7