Gauss and p-adic numbers

Franz Lemmermeyer

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arXiv · 2510.11559

Gauss and p-adic numbers

Franz Lemmermeyer

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Abstract

In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of $5$ in the $11$-adic integers in order to find an $11$-adic approximation to a quadratic Gauss sum, computes a nontrivial square root of $1$ in $10$-adic integers, and computes the $10$-adic logarithms of small natural numbers.

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Franz Lemmermeyer. 2025-10-13. Gauss and p-adic numbers. https://arxiv.org/abs/2510.11559

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