MathDB
\frac{1}{x^2}+\frac{y}{xz}+\frac{1}{z^2}=\frac{1}{2013}

Source: JBMO Shortlist 2013 NT5

April 24, 2019
number theoryDiophantine equationpositive integers

Problem Statement

Solve in positive integers: 1x2+yxz+1z2=12013\frac{1}{x^2}+\frac{y}{xz}+\frac{1}{z^2}=\frac{1}{2013} .