16 citations · 19 across the 6 of their papers we have counts for
9 papers
Polynomial equations modulo prime numbers
Arnaud Bodin, Pierre Dèbes, Salah Najib
We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers . We offer an elementary approach based on a counting metho…
The Hilbert-Schinzel specialization property
Arnaud Bodin, Pierre Dèbes, Joachim König +1
We establish a version "over the ring" of the celebrated Hilbert Irreducibility Theorem. Given finitely many polynomials in variables, with coefficients in , of po…
The relative Schinzel hypothesis
Arnaud Bodin, Pierre Dèbes, Salah Najib
The Schinzel Hypothesis is a conjecture about irreducible polynomials in one variable over the integers: under some standard condition, they should assume infinitely many prime val…
Prime and coprime values of polynomials
Arnaud Bodin, Pierre Dèbes, Salah Najib
The Schinzel Hypothesis is a celebrated conjecture in number theory linking polynomial values and prime numbers. In the same vein we investigate the common divisors of values $P_1(…
The Schinzel Hypothesis for Polynomials
Arnaud Bodin, Pierre Dèbes, Salah Najib
The Schinzel hypothesis is a famous conjectural statement about primes in value sets of polynomials, which generalizes the Dirichlet theorem about primes in an arithmetic progressi…
Families of polynomials and their specializations
Arnaud Bodin, Pierre Dèbes, Salah Najib
For a polynomial in several variables depending on some parameters, we discuss some results to the effect that for almost all values of the parameters the polynomial is irreducible…