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

Proposition: Complete and Reduced Residue Systems (Revised)

Let $a > 0$ and $b > 0$ be positive integers which are co-prime $a\perp b.$ Then the integer $ax+by$ runs through all values of

  • a complete residue system modulo $ab,$ if the integers $x$ (respectively $y$) run through all values of the complete residue systems modulo $a$ (respectively $b,$)
  • a reduced residue system modulo $ab,$ if the integers $x$ (respectively $y$) run through all values of the reduced residue systems modulo $a$ (respectively $b.$)

| | | | | created: 2019-04-29 17:21:20 | modified: 2019-04-29 17:31:07 | by: bookofproofs | references: [1272], [8152]

1.Proof: (related to "Complete and Reduced Residue Systems (Revised)")


This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:

(none)

Bibliography (further reading)

[8152] Jones G., Jones M.: “Elementary Number Theory (Undergraduate Series)”, Springer, 1998

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

FeedsAcknowledgmentsTerms of UsePrivacy PolicyImprint
© 2018 Powered by BooOfProofs, All rights reserved.