ON THE REPRESENTATIONS OF xy + yz + zx

JONATHAN BORWEIN AND KWOK-KWONG STEPHEN CHOI

Abstract. We show that there are at most 19 integers that are not of the form xy + yz + xz with x, y, z ≥ 1. Eighteen of them are small and easily found. The remaining possibility must be greater than 10^{11} and cannot occur if we assume the Generalized Riemann Hypothesis.