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arXiv · 2409.14375

Short Solutions To Homogenous Linear congruences

Omer Simhi
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Abstract

Str\"ombergsson and Venkatesh proved that a system of homogeneous linear congruence modulo prime has a positive probability to have a short non-trivial solution. We extend this result and show that the same holds for square-free moduli. In the case of 2-variables single linear congruence, we show that there is a positive probability to have a short solution for all integer moduli as well as positive probability for having short non-trivial solutions which are primitive in a suitable sense.

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Omer Simhi. 2024-09-22. Short Solutions To Homogenous Linear congruences. https://arxiv.org/abs/2409.14375

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