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arXiv · 2104.04367

On the multiplicative group generated by two primes in $\mathbf{Z}/Q\mathbf{Z}$

Péter P. Varjú
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Abstract

We study the action of the multiplicative group generated by two prime numbers in $\mathbf{Z}/Q\mathbf{Z}$. More specifically, we study returns to the set $([-Q^\varepsilon,Q^\varepsilon]\cap \mathbf{Z})/Q\mathbf{Z}$. This is intimately related to the problem of bounding the greatest common divisor of $S$-unit differences, which we revisit. Our main tool is the $S$-adic subspace theorem.

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Péter P. Varjú. 2021-04-09. On the multiplicative group generated by two primes in $\mathbf{Z}/Q\mathbf{Z}$. https://arxiv.org/abs/2104.04367

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