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Math Help - Is there a fast way to solve this system of congruences on paper?

  1. #1
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    Is there a fast way to solve this system of congruences on paper?

    x = 9 (mod 10)
    x = 8 (mod 9)
    x = 7 (mod 8)
    x = 6 (mod 7)
    x = 5 (mod 6)
    x = 4 (mod 5)
    x = 3 (mod 4)
    x = 2 (mod 3)
    x = 1 (mod 2)

    This is part of a homework word problem from my class. I don't think the Chinese remainder theorem works since the modulo are not pairwise relatively prime. The only way I can think of solving it would take 30 minutes at least without a computer. So I'm wondering if there is a better way.

    edit: I proved this must be one less than the least common multiple, i.e.
    2519 (mod 2520)
    Last edited by paulrb; October 19th 2010 at 09:36 PM.
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