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Math Help - finding rational solutions for each value of n

  1. #1
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    finding rational solutions for each value of n


    how i can solve it? plz guide me...
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  2. #2
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    A quick question - I'm assuming n is a positive integer. Is there any higher limit for n?
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  3. #3
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    First you need to show that any rational solution must be an integer.
    I think it is worth taking 1,2,3 as special cases because in that range there are some solutions.
    Now rearrange the equation as x^n+x^n-1...+x+1 = 4.

    Then note that the LHS is (x^(n+1)-1)/(x-1) (either by using the formula for the sum of a geometric series or remembering how to factorise x^n-1). This is OK because x=1 is
    never going to be a solution for n>=4.
    Now you should be easily able to show that there can be no solutions for n>=4 by considering the possible values for the LHS at integer values.
    Last edited by alunw; November 5th 2009 at 06:52 AM. Reason: rogue - removed!
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  4. #4
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    Quote Originally Posted by Debsta View Post
    A quick question - I'm assuming n is a positive integer. Is there any higher limit for n?

    no there is no higher limit for n, n is natural.
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