Does anyone know any references/hints for the following problem?

For any $k \geq 1$ there is a threshold, $n_{0}=n_{0}(k)$ such that if $n \geq n_{0}$ then any $k$ -colouring of the first $n$ integers contains three numbers $x, y, z \in[n]$ from the same colour class giving solution to the $x+y=z^2$?