Results 1 to 2 of 2

Math Help - Pythagorean Triples

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    144

    Pythagorean Triples

    Find all of the Pythagorean triples that consist of consecutive positive integers. Prove that you have found them all.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    626
    Hello, MATNTRNG!

    Find all of the Pythagorean triples that consist of consecutive positive integers.
    Prove that you have found them all.

    Let the triple be: . (a,\:a+1,\:a+2)

    Then we have: . a^2 + (a+1)^2 \;=\;(a+2)^2

    . . . . . . . . . a^2 + a^2 + 2a + 1 \;=\;a^2+4a+4

    . . . . . . . . . . . . a^2 - 2a - 3 \:=\:0

    . . . . . . . . . . (a+1)(a-3) \:=\:0

    . . . . . . . . . . . . . . . . . . . a \:=\:\text{-}1,\:3


    Since \,a is a positive integer, a = 3.

    Therefore, the only Pythagorean triple is: . (3,\,4,\,5)

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pythagorean triples
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: June 20th 2011, 03:58 AM
  2. pythagorean triples
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 23rd 2009, 08:15 PM
  3. Pythagorean triples
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 17th 2009, 05:06 PM
  4. Pythagorean Triples
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 8th 2008, 10:18 PM
  5. pythagorean triples
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 2nd 2008, 04:28 AM

Search Tags


/mathhelpforum @mathhelpforum