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Avinash
Lv 7
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 65 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.
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