Prove if (a,p)=1, then {a,2a,3a,…,pa} is a complete residue system modulo p.

Question

I'm having a hard time proving this, and I'm not sure where to start. Help appreciated

Hint: Show that if $1\le k\lt l\le p$, then $ka\not\equiv la\pmod{p}$, meaning that $p$ does not divide $la-ka$. — André Nicolas, Mar 18 '15 at 01:35

score 1 · Answer 1 · answered Mar 18 '15 at 01:37

1

Show that if $am\equiv an\pmod{p}$ then $m\equiv n\pmod{p}$.

answered Mar 18 '15 at 01:37

Thomas Andrews

1 Answers1