Earlier this week, a math puzzle that had stumped mathematicians for decades was finally solved. It’s called a Diophantine Equation, and it’s sometimes known as the “summing of three cubes”: Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100. Please Help And Thank You
Answers
[(k,x,y,z) for k in range(1,100) for x in range(10) for y in range(10) for z in range(10) if x**3 + y**3 + z**3 == k]
[(1, 0, 0, 1), (1, 0, 1, 0), (1, 1, 0, 0), (2, 0, 1, 1), (2, 1, 0, 1), (2, 1, 1, 0), (3, 1, 1, 1), (8, 0, 0, 2), (8, 0, 2, 0), (8, 2, 0, 0), (9, 0, 1, 2), (9, 0, 2, 1), (9, 1, 0, 2), (9, 1, 2, 0), (9, 2, 0, 1), (9, 2, 1, 0), (10, 1, 1, 2), (10, 1, 2, 1), (10, 2, 1, 1), (16, 0, 2, 2), (16, 2, 0, 2), (16, 2, 2, 0), (17, 1, 2, 2), (17, 2, 1, 2), (17, 2, 2, 1), (24, 2, 2, 2), (27, 0, 0, 3), (27, 0, 3, 0), (27, 3, 0, 0), (28, 0, 1, 3), (28, 0, 3, 1), (28, 1, 0, 3), (28, 1, 3, 0), (28, 3, 0, 1), (28, 3, 1, 0), (29, 1, 1, 3), (29, 1, 3, 1), (29, 3, 1, 1), (35, 0, 2, 3), (35, 0, 3, 2), (35, 2, 0, 3), (35, 2, 3, 0), (35, 3, 0, 2), (35, 3, 2, 0), (36, 1, 2, 3), (36, 1, 3, 2), (36, 2, 1, 3), (36, 2, 3, 1), (36, 3, 1, 2), (36, 3, 2, 1), (43, 2, 2, 3), (43, 2, 3, 2), (43, 3, 2, 2), (54, 0, 3, 3), (54, 3, 0, 3), (54, 3, 3, 0), (55, 1, 3, 3), (55, 3, 1, 3), (55, 3, 3, 1), (62, 2, 3, 3), (62, 3, 2, 3), (62, 3, 3, 2), (64, 0, 0, 4), (64, 0, 4, 0), (64, 4, 0, 0), (65, 0, 1, 4), (65, 0, 4, 1), (65, 1, 0, 4), (65, 1, 4, 0), (65, 4, 0, 1), (65, 4, 1, 0), (66, 1, 1, 4), (66, 1, 4, 1), (66, 4, 1, 1), (72, 0, 2, 4), (72, 0, 4, 2), (72, 2, 0, 4), (72, 2, 4, 0), (72, 4, 0, 2), (72, 4, 2, 0), (73, 1, 2, 4), (73, 1, 4, 2), (73, 2, 1, 4), (73, 2, 4, 1), (73, 4, 1, 2), (73, 4, 2, 1), (80, 2, 2, 4), (80, 2, 4, 2), (80, 4, 2, 2), (81, 3, 3, 3), (91, 0, 3, 4), (91, 0, 4, 3), (91, 3, 0, 4), (91, 3, 4, 0), (91, 4, 0, 3), (91, 4, 3, 0), (92, 1, 3, 4), (92, 1, 4, 3), (92, 3, 1, 4), (92, 3, 4, 1), (92, 4, 1, 3), (92, 4, 3, 1), (99, 2, 3, 4), (99, 2, 4, 3), (99, 3, 2, 4), (99, 3, 4, 2), (99, 4, 2, 3), (99, 4, 3, 2)]
Answer:
It took 65 years
Step-by-step explanation:
x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631.