Problem 39

Problem 39

14 March 2003

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p 1000, is the number of solutions maximised?

def fun39():
    result = (0, 0)
    #a**2+b**2=c**2,a<=b
    (a,b,c)=(1,2,3)
    for p in range(4, 1000):
        count = 0
        for a in range(1, p/3):
            t = (a**2)%(p-a)
            if t != 0:
                continue
            else:
                t = (a**2)/(p-a)
                if (t+p-a)%2 == 0:
                    (b,c) = ((p-a-t)/2, (t+p-a)/2)
                    if b < a:
                        break
                    else:
                        count += 1
                        print a,b,c
        if count > result[1]:
            result = (p, count)
    return result

answer is 840, 共有8组
time:0.125