Results 1 to 2 of 2

Math Help - natural number problem

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    2

    Exclamation natural number problem

    Let A and B be two Natural Numbers. Suppose the remainder when A is divided by n is a and the remainder when B is divided by n is b. How does the remainder when A x B is divided by n compare to the remainders a and b? Can the remainder of A x B divided by n be determined by just considering a and b? If so, prove your theory.

    Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by kelly1183 View Post
    Let A and B be two Natural Numbers. Suppose the remainder when A is divided by n is a and the remainder when B is divided by n is b. How does the remainder when A x B is divided by n compare to the remainders a and b? Can the remainder of A x B divided by n be determined by just considering a and b? If so, prove your theory.

    Thanks!!
    Symbolically,

    A \equiv a\ (\text{mod }n)
    B \equiv b\ (\text{mod }n)
    AB \equiv \ ?\ (\text{mod }n)

    The answer is known to be

    AB \equiv ab\ (\text{mod }n)

    To prove, just write

    A = k_1n + a
    B = k_2n + b

    and expand the product AB.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 14th 2011, 03:46 AM
  2. Every natural number is sum of powers of 2
    Posted in the Number Theory Forum
    Replies: 23
    Last Post: January 13th 2010, 11:58 PM
  3. Prove natural number
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 25th 2009, 10:55 AM
  4. The natural number p is prime
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 11th 2009, 09:16 AM
  5. Natural log of a negative number
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 19th 2007, 03:05 PM

Search Tags


/mathhelpforum @mathhelpforum