# Homework Help: 2^m = 3^n +5

1. Sep 24, 2004

### PrudensOptimus

Hello,

2^m = 3^n + 5, given m,n >=0

... Find all possible m,n... Any ideas?

2. Sep 24, 2004

### Hurkyl

Staff Emeritus
Try looking at it in varios moduli?

3. Sep 25, 2004

### PrudensOptimus

what does that mean lol pls explain.

4. Sep 25, 2004

### Hurkyl

Staff Emeritus
For example, if you reduce the equation mod 2^m, and there are no values of n such that 3^n + 5 = 0 (mod 2^m), then you've found an upper limit for m.

I don't know if this will work...

5. Sep 25, 2004

### Tide

$$2^m - 2 = 3^n + 3$$
That might provide some insight.

6. Sep 26, 2004

### robert Ihnot

Well, two small solutions are: 2^3 = 3+5; 2^5=3^3+5.

7. Sep 26, 2004

### devious_

Try looking up Stroeker and Tijdeman's theorem (a.k.a. the solution to Pillai's conjecture).