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- W4287998369 abstract "For finitely generated subgroups $W_1, ldots , W_t$ of $mathbb{Q}^{times}$, integers $k_1, ldots , k_t$, a Galois extension $F$ of $mathbb{Q}$ and a union of conjugacy classes $C subset text{Gal}(F/mathbb{Q})$, we develop methods for determining if there exists infinitely many primes $p$ such that the index of the reduction of $W_i$ modulo $p$ divides $k_i$ and such that the Artin symbol of $p$ on $F$ is contained in $C$. The results are a multivariable generalization of H.W. Lenstra's work. As an application, we determine all integers $a_1, ldots , a_n$ such that $text{ord}_p(a_1) = ldots = text{ord}_p(a_n)$ for infinitely many primes $p$. We also discuss the set of those $p$ for which $text{ord}_p(a_1) > ldots > text{ord}_p(a_n)$. The obtained results are conditional to a generalization of the Riemann hypothesis." @default.
- W4287998369 created "2022-07-26" @default.
- W4287998369 creator A5069118466 @default.
- W4287998369 date "2019-12-05" @default.
- W4287998369 modified "2023-09-24" @default.
- W4287998369 title "Equality of orders of a set of integers modulo a prime" @default.
- W4287998369 doi "https://doi.org/10.48550/arxiv.1912.02554" @default.
- W4287998369 hasPublicationYear "2019" @default.
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