1. The problem statement, all variables and given/known data prove that if p is a prime number and a is any integer p|/a(p does not divide a), then the additive order of a modulo p is equal to p. 2. Relevant equations 3. The attempt at a solution I know p|/ a says a[tex]\neq[/tex]pn for an integer n. The additive order of a modulo n is the smallest positive solution to ax[tex]\equiv[/tex]0 mod n. Let p be a prime number and p|/ a. Then we can say (p, a)=1. That is p and a are relatively prime. That's as far as I got.