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Math Help - Remainder problem

  1. #1
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    Remainder problem

    An integer when divided by 3 gives remainder 2, when divided by 4 gives remainder 1 ,when divided by 7 gives remainder 4. What will be the remainder when the integer divides 84 ?

    I have no clue of how to go about in solving this. Need some help


    Thanks in advance.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Arka View Post
    An integer when divided by 3 gives remainder 2, when divided by 4 gives remainder 1 ,when divided by 7 gives remainder 4. What will be the remainder when the integer divides 84 ?

    I have no clue of how to go about in solving this. Need some help


    Thanks in advance.




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  3. #3
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    I have a confusion regarding how you went from step 5 to step 6 and from step 11 to step 12 . Would you please explain ? I mean what logic or theorem did you use ?
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  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by Arka View Post
    I have a confusion regarding how you went from step 5 to step 6 and from step 11 to step 12 . Would you please explain ? I mean what logic or theorem did you use ?
    Alexmahone used the fact that


    So when you multiply by 3 you get



    Negative 3 and 1 are in the same equivalence class mod 4
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