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Thread: 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.
    $\displaystyle x \equiv 0 mod(5)$
    $\displaystyle x + 1 \equiv 0 mod(7)$
    $\displaystyle x + 2 \equiv 0 mod(9)$

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

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

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

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