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Math Help - Chinese remainder theorem

  1. #1
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    Chinese remainder theorem

    why there is not such number x in N:
    x=2(mod6)
    x=0(mod15)
    x=4(mod7)
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  2. #2
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    Quote Originally Posted by cvcv49 View Post
    why there is not such number x in N:
    x=2(mod6)
    x=0(mod15)
    x=4(mod7)

    If x=2\!\!\!\pmod 6 then x is even, and if also x=0\!\!\!\pmod {15} then it must be an even multiple of 15. But even multiples of 15 are multiples of 6 so...

    The CRT doesn't apply here since gcd(6,15)\neq 1

    Tonio
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by cvcv49 View Post
    why there is not such number x in N:
    x=2(mod6)
    x=0(mod15)
    x=4(mod7)
    Hint: the moduli must be pairwise relatively prime.
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