Question 129
Determine the largest positive integer $n$ such that there exist positive integers $x, y, z$ so that
$$
n^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 z x+3 x+3 y+3 z-6
$$
$$
n^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 z x+3 x+3 y+3 z-6
$$
MathNet 2007-part-03 — 185 problems (EN–VI) Question 129
Math Olympiad Vault · MathNet 2007-part-03 — 185 problems (EN–VI)