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Let a be an integer, then there are integers X, Y such that aX+(a+1)Y=1.

Find the smallest positive value of Y.

  • Math -

    aX + aY + a = 1
    a = 1/(X+Y+1)
    The only way that a can be an integer is for
    X+Y+1 = 1 , to get 1/1
    X = -Y

    so X and Y must be opposite integers, and of course the smallest positive integer possible for X is 1

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