论文标题
在带有根部Modulo的多项式上几乎所有素数
On polynomials with roots modulo almost all primes
论文作者
论文摘要
如果具有有限数量的素数，但没有整数根，则称其为root modulo，但没有整数。我们对所有不可约的元整数多项式$ h $进行分类，其中有一种不可约的二次二次$ g $，使得产品$ gh $非常出色。我们构建具有$ x^{p} -b $，$ p $ prime和$ b $ square的所有因素的杰出多项式。
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 polynomials $h$ for which there is an irreducible monic quadratic $g$ such that the product $gh$ is exceptional. We construct exceptional polynomials with all factors of the form $X^{p}-b$, $p$ prime and $b$ square free.
