number theory

posted by .

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 -

    Hint: Chinese Remainder Theorem

  • number theory -

    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

First Name
School Subject
Your Answer

Similar Questions

  1. 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?
  2. 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 …
  3. 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 …
  4. 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.
  5. 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.
  6. 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?
  7. 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?
  8. 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.
  9. 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 remainder …
  10. 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 – …

More Similar Questions