Posted by **john** on Wednesday, August 1, 2012 at 9:20pm.

Find the least positive integer that leaves the remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8 when divided by 11

- number theory -
**Count Iblis**, Wednesday, August 1, 2012 at 9:44pm
Hint: Chinese Remainder Theorem

- number theory -
**MathMate**, Wednesday, August 1, 2012 at 9:49pm
You can try the CRT (Chinese remainder theorem).

Master sun proceeded as follows:

Given

N≡3 mod 7

N≡4 mod 9

N≡8 mod 11

We need to find the smallest positive N.

First we find the unit remainders,

99≡1 mod 7 (99 is product of 9*11_

154≡1 mod 9 (154 is multiple of 7*11)

441≡1 mod 11 (441 is multiple of 7*9)

N mod(7*9*11) is the required number such that

N=3*99+4*154+8*441 mod 693

=4441 mod 693

=283

Check:

283≡3 mod 7

283≡4 mod 9

283≡8 mod 11 Yeah!

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