p is prime and a group of 2p - 2 number

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This is a question that I see in a book. I translate it and ask it here. my Mathematical ability is not good.



if $p$ is prime, we have $2p-2$ natural number that if we choose any $p$ of them (call S), the sum of numbers in S can not be divisible by $p$. Is below statement true?



for each $1 le i le p -1$ we have $p - 1$ numbers which sum of them is M and $Mequiv ipmod p$



Thanks.







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    up vote
    2
    down vote

    favorite












    This is a question that I see in a book. I translate it and ask it here. my Mathematical ability is not good.



    if $p$ is prime, we have $2p-2$ natural number that if we choose any $p$ of them (call S), the sum of numbers in S can not be divisible by $p$. Is below statement true?



    for each $1 le i le p -1$ we have $p - 1$ numbers which sum of them is M and $Mequiv ipmod p$



    Thanks.







    share|cite|improve this question






















      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      This is a question that I see in a book. I translate it and ask it here. my Mathematical ability is not good.



      if $p$ is prime, we have $2p-2$ natural number that if we choose any $p$ of them (call S), the sum of numbers in S can not be divisible by $p$. Is below statement true?



      for each $1 le i le p -1$ we have $p - 1$ numbers which sum of them is M and $Mequiv ipmod p$



      Thanks.







      share|cite|improve this question












      This is a question that I see in a book. I translate it and ask it here. my Mathematical ability is not good.



      if $p$ is prime, we have $2p-2$ natural number that if we choose any $p$ of them (call S), the sum of numbers in S can not be divisible by $p$. Is below statement true?



      for each $1 le i le p -1$ we have $p - 1$ numbers which sum of them is M and $Mequiv ipmod p$



      Thanks.









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 12 at 5:44









      Amin Borjian

      906




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