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Pythagorean Triples

  • 31-12-2010 3:27am
    #1
    Tillotson
    Registered Users, Registered Users 2 Posts: 218 ✭✭


    I want to generate a list of all primitive pythagorean triples limited by perimeter.
    To generate triples I can use the formula: 
    (a, b, c) = (m^2 - n^2, 2mn, m^2 + n^2)
where m > n, m and n are coprime and m or n are even.

    Perimeter = a + b + c = 2m(m + n)
    ptriples p      = [(m^2-n^2, 2*m*n, m^2+n^2) |
                        n <- [1..??],
                        m <- [n+1, n+3..??],
                        coprime m n,
                        2 * m * (m + n) < p]
    (sorry about the code, I don't know the mathematical notation)
    How do I work out the upper bounds of m and n ("??" above)?


    Edit (think I figured out m):
    a + b + c = p
    max c = p/2
    c = m^2 + n^2
    p/2 = m^2 + n^2
    max m when n = 1
    max m = floor (sqrt (p/2 - 1))

    Does this make sense?


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