a^2 + b^2 = ab^2 + 1
1 - a^2 = b^2 - ab^2
1 - a^2 = b^2 ( 1 - a)
(1 - a^2) / ( 1 - a) = b^2
[ ( 1 - a) ( 1 + a) ] / ( 1 -a) = b^2
1 + a = b^2
sqrt ( 1 + a) = b or - sqrt ( 1 + a) = b
There are infinite integer values that make this true.....Ex :
a b
-1 0
3 2
3 -2
8 -3
8 3
etc.