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Math Help - Number Theory

  1. #1
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    Number Theory

    If a number is divided by 15 , it leaves a remainder of 7. If thrice the number is divided by 5,then what is the remainder ???

    Ans. - 1 why ?

    Confusion here =>

    N/15 = 15k + 7

    Multiplying both side by 9

    3N/5 = 5 (27k)+63 ;

    3N/5 = 5 K + 3 ;

    so remainder should be 3


    What to do??
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  2. #2
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    Re: Number Theory

    Quote Originally Posted by timkuc View Post
    If a number is divided by 15 , it leaves a remainder of 7. If thrice the number is divided by 5,then what is the remainder ???

    Ans. - 1 why ?

    Confusion here =>

    N/15 = 15k + 7

    Multiplying both side by 9

    3N/5 = 5 (27k)+63 ;

    3N/5 = 5 K + 3 ;

    so remainder should be 3


    What to do??
    You should have N=15k+7

    and then 3N=45k+21

    and so 3N=5 (9k+4) + 1.
    Thanks from timkuc
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  3. #3
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    Re: Number Theory

    shame on me.. hattttt



    btw thanks
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  4. #4
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    Re: Number Theory

    N \equiv 7 (\mod 15), so it follows that N \equiv 7 \equiv 2 (\mod 5).


    Therefore, 3N \equiv 6 \equiv 1 (\mod 5) so a remainder of 1 results.
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