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# Common prime factors of $a^n-b$ and $c^n-d$

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Author(s): Christian Ballot | Florian Luca

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 2;
Issue: 2;
Start page: 19;
Date: 2007;
In this note, we study the set of primes such that the two congruences $a^n\equiv b\pmod p$ and $c^n\equiv d \pmod p$ have a simultaneous solution $n$ under some assumptions on the rationals $a, b, c, d$.
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