Local and global methods in arithmetic (in Russian)

2007/09/11 by Alexei Panchishkin, Panchishkin, Alexei
Mathematics · #11G40 #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11G40

paper · pdf · doi:10.48550/arxiv.0709.1606

in Russian, 27 pages, 5 figures

arxiv created 2007/09/11 · openalex publication_date 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime. We discuss methods of solution of congruences modulo pⁿ using p-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are given producing a passage from congruences to solutions in integers (global methods). The use of a computer is illistrated for the study of p-adic numbers and algebraic curves.

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