# Unique Factorization Prime/Co-Prime

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1. Prove that a and b are coprime if and only if no prime numbers divides both a and b

2. Show that [a,m] = m if and only if a divides m

https://brainmass.com/math/number-theory/unique-factorization-prime-co-prime-527365

#### Solution Preview

For question 1. Recall, two numbers are called co-prime when their greatest common divisor gcd(a,b)=1 (Some might use (a,b), it's just a matter of notation). Now let's think about this: suppose there exists a prime that divides both a and b, then p is a common divisor of a,b. ...

#### Solution Summary

In a few paragraphs, the solution gives a detailed explanation on how to approach problems related to primes and co-primes.

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