Local and global methods in arithmetic (in Russian)

Details Local and global methods in arithmetic (in Russian) Local and global methods in arithmetic (in Russian)

2007-09-11

arxiv.org/abs/0709.1606v1

Mathematics

Number Theory

in Russian, 27 pages, 5 figures

Scientific paper

Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ 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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