# Abelian Groups in Rational Number Theory

Chapter

## Abstract

In the elementary theory of rational numbers we are constantly dealing with Abelian groups. The set of integers has the properties:

- (i)
*a*+*b*is an integer if*a*and*b*are integers;*a*+*b*=*b*+*a*, - (ii)
*a*+ (*b*+*c*) = (*a*+*b*) +*c*, - (iii)
If

*a*+*b*=*a*′ +*b*, then*a*=*a*′, - (iv)
For each

*a*and*b*there is an integer*x*such that*a*+*x*=*b*.

## Keywords

Abelian Group Residue Class Quadratic Residue Residue Character Residue Symbol
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1981