number theory

Pythagorean Triple Problem in Sub-linear Time

The Pythagorean triple problem is as follows. Given an input integer \(n\), return integers \(a\), \(b\), \(c\) such that the two following conditions hold: $$ a b c = n $$ $$ a^2 + b^2 = c^2 $$ I was interested in finding a solution to this problem that was both succint and had good asymptotic complexity. The solution I found runs in O(sqrt(n)) time by deconstructing the problem into the well-known 3SUM problem.