Q for X

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G.C.D of (m,n)=1

1) x â‰¡3 (mod n)
x â‰¡2 (mod m)

Find x.

Got it from a frnd.

#Mathematics #Olympiad Stuff

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6 Answers

21

Arnab Kundu ·2012-01-26 07:00:58

Use Chinese remainder Theorem
http://www.cut-the-knot.org/blue/chinese.shtml

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1

Nana Dubey ·2012-01-26 10:16:59

Hey I never heard of a chinese reminder theorem ..? is it in a chinese menu ? lols..
ok jokes apart do tell me in simple terms
thank you

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21

Arnab Kundu ·2012-01-27 05:32:27

Folow the link please to get the answers to your questions

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7

Sigma ·2012-01-27 08:08:59

Well, this q was asked in The kvpy interview to a cls 11 student.

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7

Sigma ·2012-01-31 06:49:37

@ Arnab, i can't get the ans.. can u give this sum a try?

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21

Arnab Kundu ·2012-01-31 10:17:31

Let integers n^-1 and m^-1 such that
nn^-1â‰¡1(mod m)
mm^-1â‰¡1(mod n)

By Chinese Remainder theorem,
xâ‰¡2nn^-1+3mm^-1(mod mn)

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Your Answer

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