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Math Help - consecutive positive

  1. #1
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    consecutive positive

    Find a set of three consecutive positive integers such that the small-
    est is a multiple of 5, the second is a multiple of 7 and the largest is amultiple
    of 9.
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  2. #2
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    Quote Originally Posted by perash View Post
    Find a set of three consecutive positive integers such that the small-
    est is a multiple of 5, the second is a multiple of 7 and the largest is amultiple
    of 9.
    x \equiv 0 mod(5)
    x + 1 \equiv 0 mod(7)
    x + 2 \equiv 0 mod(9)

    Can you solve that system of congruences?
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  3. #3
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    Quote Originally Posted by colby2152 View Post
    x \equiv 0 mod(5)
    x + 1 \equiv 0 mod(7)
    x + 2 \equiv 0 mod(9)

    Can you solve that system of congruences?
    Yes.
    This is equivalent too.
    x\equiv 0(\bmod 5)
    x\equiv 6(\bmod 7)
    x\equiv 7(\bmod 9).

    Using the Chinese remainder theorem (details ommited) all the numbers that satisfy this are: 315k+160 where k\in \mathbb{Z}.

    This is Mine 9th Post!!!
    Last edited by ThePerfectHacker; March 17th 2008 at 06:50 PM.
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