Question on solution for 2013 USAJMO #1 The problem and solution can be viewed here
My question is on the part where they state

If $a^5b\equiv 6\pmod 9$, then note that $3|b$. This is because if
  $3|a$ then $a^5b\equiv 0\pmod 9$.

I don't understand how they got that b is divisible by 3. Can someone please explain?

From $a^5b \equiv 6\pmod 9$ we have that $3 | a^5b$. So it must be true that either $3 | a$ or $3 |b$. But $3$ cannot divide $a$ for if it does then $9 | a^5$ and therefore $9 | a^5b$ which contradicts $a^5b \equiv 6\pmod 9$
