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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.
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Minimal root of $f(x)$ mod $p$
Let $f(x)$ be an irreducible integral polynomial with degree $\text{deg}[f]$. If $p|f(x)$ for some $x$, then denote by $S(p)$ the smallest positive number $x_0$ such that $p | f(x_0)$.
Do there exist …