Title: Majoration du nombre de valeurs friables d'un polynôme,
Abstract: For $Q$ a polynomial with integer coefficients and $x, y \geq 2$, we prove
upper bounds for the quantity $\Psi_Q(x, y) = |\{n\leq x: p\mid Q(n)\Rightarrow
p\leq y\}|$.
We apply our results to a problem of De Koninck, Doyon and Luca on integers
divisible by the square of their largest prime factor. As a corollary to our
arguments, we improve the known level of distribution of the set $\{n^2-D\}$
for well-factorable moduli, previously due to Iwaniec. We also consider the
Chebyshev problem of estimating $\max\{P^+(n^2-D), n\leq x\}$ and make
explicit, in Deshouillers-Iwaniec's state-of-the-art result, the dependence on
the Selberg eigenvalue conjecture.