Can this equation be solved using integer numbers?

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SUMMARY

The equation 3x = 4y + 5 can be analyzed for integer solutions by expressing one variable in terms of the other. The key condition for integer solutions is derived from modular arithmetic, specifically 3x ≡ 1 (mod 4). Utilizing Fermat's Little Theorem, it is established that if x = 3, the equation simplifies to a single variable equation, facilitating the search for integer solutions.

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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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