Question 24
Determine all pairs $(x, y)$ of positive integers such that
$$
\sqrt[3]{7 x^{2}-13 x y+7 y^{2}}=|x-y|+1
$$
$$
\sqrt[3]{7 x^{2}-13 x y+7 y^{2}}=|x-y|+1
$$
IMO 2014 — Complete Shortlist Question 24
IMO Shortlist · IMO 2014 — Complete Shortlist