Gauss and p-adic numbers
arXiv:2510.11559
Abstract
In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of in the -adic integers in order to find an -adic approximation to a quadratic Gauss sum, computes a nontrivial square root of in -adic integers, and computes the -adic logarithms of small natural numbers.