Abstract Algebra Proof: If k = abc + 1, then prove that (k,a) = (k,b) = (k,c) = 1?

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  • Awms A
    Lv 7
    8 years ago
    Favorite Answer

    If d divides both k and one of a,b,c, then d divides

    k - abc = 1.

    If d is a positive integer, this implies d = 1.

    Now apply that to the gcd's.

  • 8 years ago

    Assume k = dx, a = dy

    then dx = dybc +1

    1 = dx - dybc

    1 = d (x - ybc), then d l 1, (x - ybc) integers

    Good Luck.

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