How many distinct pairs of perfect squares differ by 35? (the pair $a, b$ is the same as the pair $b, a$.) ?

35 has 4 divisors, hence two factor pairs: 1*35 and 5*7. Each corresponds to a set of perfect squares that differ by 35

One pair is ((35±1) / 2) ^2 = {17^2, 18^2} = {289, 324}

The other is ((7±5) / 2) ^2 = {1^2, 6^2} = {1, 36}