MathDB
The identity gives perfect square

Source: Greek TST 2018

April 2, 2019
functionnumber theory

Problem Statement

Find all functions f:Z>0↦Z>0f:\mathbb{Z}_{>0}\mapsto\mathbb{Z}_{>0} such that
xf(x)+(f(y))2+2xf(y)xf(x)+(f(y))^2+2xf(y) is perfect square for all positive integers x,yx,y.
**This problem was proposed by me for the BMO 2017 and it was shortlisted. We then used it in our TST.
Back to ProblemsView on AoPS