MATH 13150: Freshman Seminar Unit 9 1. More on prime numbers
... the difference of two multiples of 3, it follows that 3 divides b.
To do this argument for a general prime p and a general number a that is not divisible
by p, note that since p does not divide a, gcd(a, p) = 1. Indeed, if a number divides
a and p, it would have to divide p, so the number would have ...