Results 1 to 6 of 6

Math Help - Finding the biggest possible value of n

  1. #1
    Member
    Joined
    Sep 2011
    Posts
    149

    Finding the biggest possible value of n

    Let n satisfy the equation, a^n+b^n=c^2. When a,b,c are prime numbers and n is an integer, there is one solution at least for the equation.

    How to find the biggest possible value of n?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    66

    Re: Finding the biggest possible value of n

    Could you give us the solution that you say exists?

    Have you managed to narrow down the possibilities for a and b?

    I have made some progress but have not found a solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2011
    Posts
    149

    Re: Finding the biggest possible value of n

    I think i solved it



    And take Mod 5 in the last equation
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    66

    Re: Finding the biggest possible value of n

    Quote Originally Posted by Mhmh96 View Post
    I think i solved it
    What's your solution?

    Quote Originally Posted by Mhmh96 View Post
    And take Mod 5 in the last equation
    Why?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    66

    Re: Finding the biggest possible value of n

    How about 2+2=4?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: Finding the biggest possible value of n

    It's really easy to show that one of a,b must be 2.

    Then use casework on the parity of n. Note that if n is odd, the LHS factors.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. the biggest area
    Posted in the Geometry Forum
    Replies: 4
    Last Post: September 2nd 2009, 12:30 AM
  2. Replies: 1
    Last Post: April 29th 2009, 08:20 AM
  3. Replies: 1
    Last Post: September 10th 2008, 02:59 PM
  4. triangle with biggest area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 23rd 2006, 06:06 PM

Search Tags


/mathhelpforum @mathhelpforum