number theory
posted by john .
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

Hint: Chinese Remainder Theorem

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!
Respond to this Question
Similar Questions

Math
What is the smallest number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, when divided by 8 leaves a remainder of 7 & so on until when divided by 2 leaves a remainder of 1? 
math
what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and … 
math
what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and … 
Algebra 2
Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5, a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11. 
Math
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. Using the Chinese Remainder Theorem. 
Math
How many integers bewteen 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4? 
Math
How many integers between 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4? 
Math
Find the smallest positive integer that leaves a remainder of 5 when divided by 7, a remainder of 6 when divided by 11, and a remainder of 4 when divided by 13. 
math
1.) when the expression 4x^23x8 is divided by xa, the remainder is 2. find the value of a. 2.) the polynomial 3x^3+mx^2+nx+5 leaves a remainder of 128 when divided by x3 and a remainder of 4 when divided by x+1. calculate the remainder … 
Math adv function
An unknown polynomial f(x) of degree 37 yields a remainder of 1 when divided by x – 1, a remainder of 3 when divided by x – 3, a remainder of 21 when divided by x – 5. Find the remainder when f(x) is divided by (x – 1)(x – …