## Online Course Discussion Forum

### Need help on math challenge II-A chapter 7 problem 7.30

Need help on math challenge II-A chapter 7 problem 7.30

Can I get a hint for this problem? I have no idea how to solve it.

Re: Need help on math challenge II-A chapter 7 problem 7.30

Hi Yizhou. Are you referring to Algebra, Geometry, Number Theory, or Combinatorics? Also, I can see you are taking some of the Math Challenge II-B, not II-A, courses as self paced, so is this for MC II-B?

Re: Need help on math challenge II-A chapter 7 problem 7.30

Sorry, I forgot to put it in my post, I meant the number theory book. Also im just reviewing my II-A book that's why.

Re: Need help on math challenge II-A chapter 7 problem 7.30

This looks a lot like Euler's Theorem (the extension of Fermat's Little Theorem), right?

Euler's Theorem guarantees that both $m^{\phi(n)} \equiv 1 \pmod{n}$ and $n^{\phi(n)} \equiv 1 \pmod{m}$. How can you turn these into something that looks like $m^{\phi(n)} + n^{\phi(m)}$?

(Try to remember what we usually do in a problem like "what is the largest three-digit number that leaves a remainder of $1$ when divided by $5$ and $7$?")