# number theory

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

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. Hint: Chinese Remainder Theorem

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. 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!

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### algebra

use the remainder theorem to find the remainder when P(x)=x^4-9x^3-5x^2-3x+4 is divided by x+3

2. ### math

1)The function f is defined by the equation f(x)+ x-x^2. Which of the following represents a quadratic with no real zeros? A)f(x) +1/2 B)f(x)-1/2 C)f(x/2) D)f(x-1/2) 2) If I^(2k) = 1, and i = radical -1, which of the following

3. ### maths

A number on being divided by 10 and 11 successively leaves the remainders 5 and 7. Find the number. ie, x/10 = remainder 5 and x/11 = remainder 7. please help me to find the value of x.

4. ### maths

ifx^3+mx^2+nx+6 has x-2 as a factor and leaves remainder 3 when divided by x-3, find the values of m and n.

1. ### Maths

When the Polynomial p(x)=ax^3+5x^2+bx-2 where a and b are constants is divided by 2x^2+3x-2, the remainder is 9x-6. (I) Find the values of a and b (II) Using these values of a and b, factorize p(x) completely (III) Find the

2. ### math

When a positive integer, n, is divided by 24 the remainder is 18. When n is divided by 8 the remainder is: A.0 B.1 C.2 D.4 E.6 I tried doing n/24=18 and I got 432 and when I divided it by 8 I got 54; am I misinterpreting the

3. ### 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.

4. ### math

1.) when the expression 4x^2-3x-8 is divided by x-a, 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 x-3 and a remainder of 4 when divided by x+1. calculate the

1. ### Algebra

If p(x) is a polynomial and is divided by (x-k) and a remainder is obtained, then that remainder is p(k). If the quadratic p(x)=x^2-3x+5 gives the same remainder when divided by x+k as it does when divided by x-3k find the value

2. ### Maths

Hi, What is the lowest positive integer greater than 1, which when divided by 5 or 8 leaves a remainder of 1 Thanks

3. ### math

The polynomial P(x)=x3−4x2−5x−42 can be rewritten as P(x)=(x−6)(x2+2x+7). What can you conclude about P(x)? There may be more than one correct answer. Select all correct answers. When P(x) is divided by x−6, the

4. ### Math

The expression ax^2 + bx + c is divisible exactly by (x - 1), has a remainder of 2 when it is divided by (x + 1), and has a remainder of 6 when it is divided by (x - 2). Find a, b and c?