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Math Help - algebra of remainders

  1. #1
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    algebra of remainders

    can some1 pls help noone can do this proof and preventing me fully understanding the chinese remainder thm

    thanx loadz
    Edgar


    z = integers

    prove the following generalisation of the Chinese Remainder Theorem. Show that if m1,m2,m3, are pairwise coprime integers and a1 is an element of z/m1 and a2 is an element of z/m2 and a3 is an element of z/m3 then there is a unique x element of z/(m1m2m3) such that

    x identical a1 mod m1
    x identical a2 mod m2
    x identical a3 mod m3
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  2. #2
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    Quote Originally Posted by edgar davids View Post
    can some1 pls help noone can do this proof and preventing me fully understanding the chinese remainder thm

    thanx loadz
    Edgar


    z = integers

    prove the following generalisation of the Chinese Remainder Theorem. Show that if m1,m2,m3, are pairwise coprime integers and a1 is an element of z/m1 and a2 is an element of z/m2 and a3 is an element of z/m3 then there is a unique x element of z/(m1m2m3) such that

    x identical a1 mod m1
    x identical a2 mod m2
    x identical a3 mod m3
    The basic theorem (Chinese Remainder) says if you are given a system:
    x\equiv a_1 (\mbox{mod } m_1)
    x\equiv a_2 (\mbox{mod } m_2)
    ................................
    x\equiv a_n (\mbox{mod } m_n)
    Then there is a unique x that satisfyies all of these congruences.
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