Can this equation be solved using integer numbers?

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The equation 3^x = 4y + 5 can be analyzed by expressing one variable in terms of the other to explore integer solutions. It is suggested to consider the equation modulo 4, leading to the condition 3^x ≡ 1 (mod 4). This relationship is connected to Fermat's Little Theorem, which indicates that x must be a multiple of 3 for integer solutions to exist. The discussion revolves around how to manipulate the equation to isolate variables effectively. Ultimately, the focus is on determining the conditions under which integer solutions are possible.
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How to solve that eqation?
3^x=4y+5
 
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Express one variable in terms of the other (see which makes most sense). What are the conditions for having integer solutions?
 
That is the same as saying that 3^x= 1 (mod 4). Check out "Fermat's Little Theorem".
 
Ok, but how can I show that this equation 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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