Periodicity in the $p$-adic valuation of a polynomial

Luis A. Medina, Victor H. Moll, Eric Rowland

For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted by ${\nu }_p(x)$. For a polynomial $Q$ with integer coefficients, the sequence of valuations ${\nu }_p(Q(n))$…