Results 1 to 3 of 3

Math Help - Proof of a Conjecture or Counter Examples

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    24
    Thanks
    1

    Proof of a Conjecture or Counter Examples

    {P-Q}{P^(n-1) + K1[P^(n-2)]Q + K2[P^(n-3)]Q^2 + ....+ Q^(n-1)} cannot equal C^n - B^n
    where all the variables are positive integers, n>2, P>Q, C>B
    unless all the Ks are equal to 1 or in some instances the Ks have the same value.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2010
    Posts
    24
    Thanks
    1

    Re: Proof of a Conjecture or Counter Examples

    Can anyone please prove or disprove this?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    52
    Thanks
    17

    Re: Proof of a Conjecture or Counter Examples

    Quote Originally Posted by MrAwojobi View Post
    {P-Q}{P^(n-1) + K1[P^(n-2)]Q + K2[P^(n-3)]Q^2 + ....+ Q^(n-1)} cannot equal C^n - B^n
    where all the variables are positive integers, n>2, P>Q, C>B
    unless all the Ks are equal to 1 or in some instances the Ks have the same value.
    For:
    P=2
    Q=1
    n=3
    K1=4
    K2=7
    C=3
    B=2 we have:

    (P - Q) \cdot \left( {{P^{n - 1}} + {K_1} \cdot {P^{n - 2}} \cdot {Q^1} + {K_2} \cdot {P^{n - 3}} \cdot {Q^2} + ... + {K_{n - 2}} \cdot {P^1} \cdot {Q^{n - 2}} + {K_{n - 1}} \cdot {Q^{n - 1}}} \right) \ne {C^n} - {B^n} \Leftrightarrow

    (2 - 1) \cdot ({2^{3 - 1}} + 4 \cdot {2^{3 - 2}} \cdot {1^1} + 7 \cdot {1^{3 - 1}}) \ne {3^3} - {2^3} \Leftrightarrow

    4 + 8 + 7 \ne 19 \Leftrightarrow

    19 \ne 19

    Obviously the conjecture can't be true.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof of a Conjecture or Counter Examples
    Posted in the Advanced Algebra Forum
    Replies: 24
    Last Post: July 24th 2013, 07:27 AM
  2. 2 problems involving examples and counter-examples.
    Posted in the Math Topics Forum
    Replies: 7
    Last Post: July 20th 2010, 11:37 AM
  3. counter examples!
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 8th 2009, 01:09 PM
  4. counter examples with real functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 17th 2007, 04:59 PM
  5. counter examples in real analysis
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 12th 2007, 06:38 AM

Search Tags


/mathhelpforum @mathhelpforum