# Math Help - Solve in integer numbers

1. ## Solve in integer numbers

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

2. $3^x\equiv 5=1 \ \mbox{(mod 4)}$

3. Ok, but what it is. How can I do i to my equation.

4. What happens when x = 2? How about x = 4? ....

5. Can you solve me a complete this equation, Step by step?

6. I pretty much solved it for you already.

When x = 2, the congruence is true.

When x = 4, it is true.

x = 6, true as well.

x = 8 guess what? True.

Notice anything?

Let's not forgot x = 0 is true too.

7. $3^{2k}=9^k\equiv 1^k=1\pmod{4}$, but $3^{2k+1}=9^k\cdot 3\equiv 3\pmod{4}$.