If $n$ is a positive integer, let $\phi(n)$ the Euler function.
( if $n=p_1^{\alpha_1}\dots p_k^{\alpha_k}$ with $p_i$ distinct primes, we have $\phi(n)=p_1^{\alpha_1-1} \dots p_k^{\alpha_k-1}(p_1-1)\dots(p_k-1)$ )
Let $P$ a polynomial in $\mathbb{Z}[X,Y]$.
We suppose there exists an infinite number of positive integer $n$ such that $P(n,\phi(n))=0$
Is $P$ reducible in factors of degree one ?
Thanks in advance.