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Find the number of ordered pairs (x,y) satisfying x2 + 1=y and y2 + 1 =x.
X^2 +1=y...(1)
y^2 +1=x...(2), (1)-(2) implies (x+y)(x-y)=-(x-y), so x+y=-1...(3)
but (1) implies y>0 and (2) implies x>0,so x+y>0, comparing this with (3), there is a contradiction. Therefore there are zero ordered pairs of real solutions.
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