Solve in integer numbers

oszust001

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

SEngstrom

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

HallsofIvy

That is the same as saying that [itex]3^x= 1[/itex] (mod 4). Check out "Fermat's Little Theorem".

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?

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oszust001	Solve in integer numbers Tweet How to solve that eqation? 3^x=4y+5

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

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	That is the same as saying that [itex]3^x= 1[/itex] (mod 4). Check out "Fermat's Little Theorem".

oszust001	Solve in integer numbers 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?