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Math Help - Solve in integer numbers

  1. #1
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    Solve in integer numbers

    How to solve that eqation?
    3^x=4y+5
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  2. #2
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    3^x\equiv 5=1 \ \mbox{(mod 4)}
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  3. #3
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    Ok, but what it is. How can I do i to my equation.
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  4. #4
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    What happens when x = 2? How about x = 4? ....
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  5. #5
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    Can you solve me a complete this equation, Step by step?
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  6. #6
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    I pretty much solved it for you already.

    When x = 2, the congruence is true.

    When x = 4, it is true.

    x = 6, true as well.

    x = 8 guess what? True.

    Notice anything?

    Let's not forgot x = 0 is true too.
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  7. #7
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    3^{2k}=9^k\equiv 1^k=1\pmod{4}, but 3^{2k+1}=9^k\cdot 3\equiv 3\pmod{4}.
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