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math.NT2022★ 3 cited
On polynomials with roots modulo almost all primes
Christian Elsholtz, Benjamin Klahn, Marc Technau
Call a monic integer polynomial exceptional if it has a root modulo all but a finite number of primes, but does not have an integer root. We classify all irreducible monic integer…
math.NT2022★ 3 cited
Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums
Paolo Minelli, Athanasios Sourmelidis, Marc Technau
We investigate the number of steps taken by three variants of the Euclidean algorithm on average over Farey fractions. We show asymptotic formulae for these averages restricted to…