# Prove that if $a \equiv b \pmod{8}$, then $2a \equiv 2b \pmod{16}$.

My professor recently assigned us a homework question but he did not cover any similar questions to it, so I do not know how to approach the problem at all.

The question is: Use the definition of congruence to prove that if $a \equiv b \pmod{8}$, then $2a \equiv 2b \pmod{16}$.

If any tips could be provided as to how to begin the problem, thanks!

• You yourself specified that this is your Homework Question, this may lead to downvotes. BTW Salute to your honesty. Apr 14, 2017 at 18:50
• Hint. Start with what the definition of congruence says about $a$, $b$ and $8$. I think that hint doesn't count as doing your homework for you. Apr 14, 2017 at 18:53
• Sorry, I was not trying to receive the full solution I just wanted some hints as to how to start the problem :( Apr 14, 2017 at 18:55
• I would say it's encouraged to say that this is homework, the community here don't like to do someones homework but like helping people do their homework Apr 14, 2017 at 19:46