# Solve in integer numbers

1. Dec 16, 2010

### oszust001

How to solve that eqation?
3^x=4y+5

2. Dec 16, 2010

### SEngstrom

Express one variable in terms of the other (see which makes most sense). What are the conditions for having integer solutions?

3. Dec 16, 2010

### HallsofIvy

Staff Emeritus
That is the same as saying that $3^x= 1$ (mod 4). Check out "Fermat's Little Theorem".

4. Dec 19, 2010

### oszust001

Ok, but how can I show that this eqation can be saying like that you wrote? If I place for 3^x=1(mod 4) to top equation and from Fermat's little theorem I have x=3 than I have equation with one variable? That you thought about?