Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

a and n are two natural numbers. Prove that if a and n are relatively prime,?

then there exists a unique natural number b < n so that ab-1 is divisible by n

Update:

Actually I have to prove ab mod(n) 1

1 Answer

Relevance
  • ?
    Lv 6
    5 years ago

    If a and n are relatively prime, then there are integers b and c such that ab + nc = 1. (Per Bezout's Lemma.)

    Then ab - 1 = -nc, so ab - 1 is divisible by n.

Still have questions? Get your answers by asking now.