# Thread: Definition of Eulers Theorem

1. ## Definition of Eulers Theorem

I'm not looking for an answer to any particular question just how to apply Eulers Theorem i know it is a to some phi(n) is congruent to 1 mod n iff (a,n) = 1. I just missed the lecture and dont understand how to apply it to these types of problems. What is the function phi and how is it used to get the least positive residue? Any clarification would be great im lost.

2. Which type of problem?

The function $\phi$ maps $n$ to the number of integers $1 \leq j \leq n$ such that $(j,n)=1$. There is a lot to be said about it, so perhaps refining your question would be good...

Have you tried reading the course material?

3. Unfortunately for me my professor does not use a book and he doesnt follow much of a lesson plan he just starts on one topic and usually spends an hour and 45 minutes talking about something else off topic. Hes brilliant but very difficult to follow and unorganized. Here are the problems i was referring to. THe first is: Complete the least positive residue of 2^(340)mod361 and the second is: Use Euler's Theorem and anything else needed, find the least positive x such that 2^6073is congruent to xmod1023