Monday, November 29, 2010

Integer as sum of cubes

Could you find an integer X that can be expressed in two different ways as the sum of three perfect cubes, that is to say

X = a^3 + b^3 + c^3 = d^3 + e^3 + f^3


And, could you find an integer Y that can be expressed in three different ways as the sum of two perfect cubes, that is to say,

Y = a^3 + b^3 = c^3 + d^3 = e^3 + f^3


Note that 1729 is the smallest number that can be expressed as the sum of two cube numbers in two different ways

1729 = 1^3 + 12^3 = 9^3 + 10^3

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