Results 1 to 3 of 3

Math Help - MATH question - induction!?

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    50

    MATH question - induction!?

    Let a,b be two positive natural numbers. Prove that for every positive odd number n, a^n + b^n is divided by a+b
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by tukilala View Post
    Let a,b be two positive natural numbers. Prove that for every positive odd number n, a^n + b^n is divided by a+b
    Hint: Prove that a^n + b^n = (a+b)\left( \sum_{k=0}^{n-1} (-1)^k a^{k-n} b^k \right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2008
    Posts
    130
    Quote Originally Posted by ThePerfectHacker View Post
    Hint: Prove that a^n + b^n = (a+b)\left( \sum_{k=0}^{n-1} (-1)^k a^{k-n} b^k \right)
    Here is the expanded notation [n is a positive odd integer]:

    a^n + b^n = (a + b)(a^{n-1} - a^{n-2}b + a^{n-3}b^2 - \cdots + a^2b^{n-3} - ab^{n-2} + b^{n-1})
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Math Induction Help
    Posted in the Pre-Calculus Forum
    Replies: 12
    Last Post: December 6th 2009, 08:19 PM
  2. Math Induction
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 1st 2008, 10:24 AM
  3. Math Induction
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: February 29th 2008, 06:40 AM
  4. math induction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 17th 2007, 08:09 AM
  5. Math Induction
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 15th 2007, 03:28 PM

Search Tags


/mathhelpforum @mathhelpforum