Revision history [back]

Elementary version

sage: for a in srange(1, 5000):
....:   for b in srange(1, a+1):
....:     for c in srange(1, b+1):
....:       if (a+b+c).is_square() and (a^2+b^2+c^2).is_square() and (a^3+b^3+c^3).is_square():
....:         print(a,b,c)

A little bit more elaborate

sage: for abc in srange(1, 10000):
....:   abc = abc*abc
....:   for a in srange((abc + 2)// 3, abc):
....:     for b in srange((abc - a + 1)//2, min(a, abc - a)):
....:       c = abc - a - b
....:       if (a^2+b^2+c^2).is_square() and (a^3+b^3+c^3).is_square():
....:         print(a,b,c)

From which you get the list: (129, 124, 108), (516, 496, 432), (1161, 1116, 972), (2873, 2134, 34), (2064, 1984, 1728), (3225, 3100, 2700), ...