剩余类中的最小对象

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-08 DOI:10.1112/blms.70069

Abhishek Jha

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引用次数: 0

摘要

我们得到了等差数列中林尼克定理的一个完整的类比。具体来说，对于任意正整数对（m, a） $(m,a)$且m $m$为奇数，存在n≤m 2 + o (1) $n\leqslant m^{2+o(1)}$使得φ (n)≡a（对m取模）$\varphi (n)\equiv a\ (\mathrm{mod}\ m)$。

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Smallest totient in a residue class

We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers $(m, a)$ such that $m$ is odd, there exists $n ⩽ m^{2 + o (1)}$ such that $φ (n) \equiv a (\mod m)$ .