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

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Mathematics

Matteo Turner

13 December, 19:01

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

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Dylan Nash · Answer 1

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}