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  • Is this a valid proof?

    Just thought of a potential proof that any nth root of 2 is irrational if n>2. I have no idea if there's some logical flaw here though, so if someone could point it out that would be great.

    Assume nroot(2) is rational.

    Then nroot(2)=a/b for some integers a, b.

    Taking each side to the nth power we get:

    2=(a/b)^n=a^n/b^n

    Multiplying by b^n:

    2b^n=a^n

    This is the same as:

    b^n+b^n=a^n

    But because of Fermat's Last Theorem this can't be true for any integer >2.

    3 AnswersMathematics7 years ago