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Math Help - Algebra Problem

  1. #1
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    Algebra Problem

    Find the smallest number, divisible by 13, such that the remainder is 1 when divided by 4,6 or 9.
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  2. #2
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    Re: Algebra Problem

    The number is congruent to 1 mod 4, 1 mod 6, 1 mod 9 so it must be congruent to 1 mod 36 (36 being lcm(4,6,9)). So we want to find integer solutions (a,b) to

    13a = 36b + 1

    If we look at this modulo 12, we see that the LHS is congruent to a and the RHS is congruent to 1. Therefore a \equiv 1 (\mod 12). a = 1, a = 13 do not work, but a = 25 works. Hence the smallest possible positive multiple of 13 that works is 13*25, or 325.
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  3. #3
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    Re: Algebra Problem

    thanks sir !
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  4. #4
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    Re: Algebra Problem

    Take out the LCM of 4,6,9
    After taking out the LCM, we get 36
    Now, add 36 with 13 = 49
    Thus, smallest number is 49.
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