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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