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[Post New]24 Apr 2008 15:27:11 IST
    Subject: question
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man111 (37)

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(1) [ i=1][ 1000] 10i is divided by 7, than find remainder.
    
[Post New]24 Apr 2008 15:51:05 IST
    Subject: Re:question
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sboosy (2860)

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10^1+10^2+10^3+10^4+....10^{1000} \ \mbox{mod} \ 7 = ? \\ \\ \mbox{Final remainder} = \mbox{Remainder obtained when S is divided by 7} \\ \\ \mbox{where S is the sum of the remainders when each number is individually divided by 7} \\ \\ 10 \ \mbox{mod} \ 7 = 3 ,\ 100 \ \mbox{mod} \ 7 = 2 ....\\ \\ \mbox{The pattern is} \ (3,2,6,4,5,1),(3,2,6,4,5,1),(3,2,6,4,5,1) .....166 \ \mbox{times} ,(3,2,6,4) \\ \\ \mbox{Sum of each bracket is} \ 21 \ \mbox{and each bracket} \\ \\ \mbox{appears 166 times(i.e) upto} \ 10^{996} \ \mbox{and for the last four} \\ \\ \mbox{we have} \ (3,2,6,4) \\ \\ \mbox{Thus the final remainder is} \ 166*21+15 \ \mbox{mod} \ 7 = 1
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