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