# Chapter 2 Equations Proved Impossible by Congruence Considerations

- Publisher
- Elsevier B.V.
- Identifiers
- DOI: 10.1016/s0079-8169(08)60003-3
- Disciplines

## Abstract

Publisher Summary This chapter discusses the equations proved impossible by congruence considerations. It also presents several theorems associated with these equations. Application of several elementary results in number theory are required to find the solutions of the equations f (x) = 0 (polynomial equations) by congruence considerations. For every natural number r, there exists a fixed set S(r) of primes such that for every prime p not in S(r), every homogenous equation f (x) = 0 of degree rand with n > r2 variables, always has a non-trivial solution in the p-adic fields.

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