Can this equation be solved using integer numbers?

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Homework Help Overview

The discussion revolves around the equation 3^x = 4y + 5, exploring whether it can be solved using integer values for x and y. The subject area includes number theory and modular arithmetic.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss expressing one variable in terms of the other and consider the conditions necessary for integer solutions. There is also a reference to modular arithmetic and Fermat's Little Theorem as a potential approach to analyze the equation.

Discussion Status

The discussion is active, with participants exploring different interpretations of the equation and questioning how to apply modular arithmetic to derive a single-variable equation. Some guidance has been offered regarding the use of modular conditions.

Contextual Notes

There is an emphasis on finding integer solutions, and participants are considering the implications of modular constraints on the original equation.

oszust001
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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 [itex]3^x= 1[/itex] (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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