2^m = 3^n + 5, given m,n >=0
... Find all possible m,n... Any ideas?
Try looking at it in varios moduli?
what does that mean lol pls explain.
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...
Try rewriting your equation as
[tex]2^m - 2 = 3^n + 3[/tex]
That might provide some insight.
Well, two small solutions are: 2^3 = 3+5; 2^5=3^3+5.
Try looking up Stroeker and Tijdeman's theorem (a.k.a. the solution to Pillai's conjecture).
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