Welcome guest
You're not logged in.
168 users online, thereof 0 logged in

## Diophantine Equations and Complete and Reduced Residue Systems

The following section is dedicated to further important concepts of elementary number theory:

• Diophantine equations, i.e. equations involving integers only,
• complete residue systems, i.e. sets of integers which represent all possible congruence classes modulo a positive integer $m > 0,$
• and reduced residue systems, i.e. complete residue systems, from which those integers have been removed, which have common divisors with $m.$

The last two concepts will help us to get deeper insights for possible solutions of Diophantine equations. Knowing the solutions of such equations often enables us to solve practical applications which can be modeled by some of these equations. We start with some definitions and basic facts about Diophantine equations.

| | | | created: 2019-04-19 06:41:31 | modified: 2019-04-19 07:05:18 | by: bookofproofs | references: [1272], [8152]

(none)