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!

## Answer this Question

## Related Questions

Math - How many integers between 200 and 500 inclusive leave a remainder 1 when ...

Math - How many integers bewteen 200 and 500 inclusive leave a remainder 1 when ...

Math - Find the least positive integer that leaves the remainder 3 when divided...

math - what is the least common positive integer that meets the following ...

math - what is the least common positive integer that meets the following ...

Math - Find the smallest positive integer that leaves a remainder of 5 when ...

Algebra 2 - Find a positive integer smaller than 500 that has a remainder of 3 ...

math - 1.) when the expression 4x^2-3x-8 is divided by x-a, the remainder is 2. ...

Math - What is the smallest number which when divided by 10 leaves a remainder ...

Math - repost for Anonymous - Can someone show me the steps to these questions (...