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?