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Math Help - Findng the remainder

  1. #1
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    Findng the remainder

    Hi Guys,

    suppose a number N when divided by numbers x and y leaves a remainder r1 and r2 respectively

    ie., N mod x = r1 and N mod y = r2

    What is N mod (x*y)

    Please help me understand the logic behind this scenario

    Thanks,
    Sai
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  2. #2
    Senior Member MacstersUndead's Avatar
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    It's been a while, but I'll take a stab at it anyway.

    "r1" and "r2" are classes of numbers.

    ex. r1 = { ... r1 - 2x, r1 - x, r1, r1 + x, r1 +2x ...}

    so,
    N mod x = r1 <=> r1 + nx = N, for n integer (1) (def'n)
    N mod y = r2 <=> r2 + my = N, for m integer (2) (def'n)
    (with n not necessarily equal to m)

    x*y = [(N-r1)(N-r2)]/nm, by (1) and (2)

    Let p = N mod(x*y) <=> p + l [[N-r1)(N-r2)]/nm] = N (def'n), for l integer.

    then p = N - (l/nm)[(N-r1)(N-r2)]
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