System of three equations - Iran First Round 2018, P14
Source:
March 7, 2021
system of equationsalgebra
Problem Statement
For how many integers does the following system of equations has a solution other than in the set of real numbers? \begin{align*} \begin{cases} a^2+b^2=kc(a+b),\\ b^2+c^2 = ka(b+c),\\ c^2+a^2=kb(c+a).\end{cases}\end{align*}