Frobenius numbers of Pythagorean triples

Abstract

Given relatively prime integers a(1) ,..., a(n), the Frobenius number g(a(1) ,..., a(n)) is defined as the largest integer which cannot be expressed as x(1)a(1)+ . . . + x(n)a(n) with x(i) nonnegative integers. In this paper, we give the Frobenius number of primitive Pythagorean triples: g(m(2) - n(2), 2mn, m(2) + n(2)) - (m - 1)(m(2) - n(2)) + (m - 1)(2mn) - (m(2) + n(2))