Triple cube sums

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What is the digit sum of the smallest number that can be expressed as the sum of two positive cubes in three different ways?


The answer is 45.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

This number is called Taxicab number . The 3rd taxicab number is...

8759319 = 16 7 3 + 43 6 3 = 22 8 3 + 42 3 3 = 25 5 3 + 41 4 3 8759319 = 167^{3} + 436^{3} = 228^{3} + 423^{3} = 255^{3} + 414^{3}

Therefore, digit sum = 45 = \boxed{45}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Taxicab numbers are actually numbers with 2 different ways to be written as the sum of two cubes. The first one is 1729, since it can be shown as twelve cubed plus one cubed and nine cubed plus ten cubed.

Sharky Kesa - 7 years, 5 months ago

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@Sharky Kesa Ummm........nope, you see the number which you are talking about is actually the Hardy Ramanujan Number(which itself is the second Taxicab number).......

Aaghaz Mahajan - 2 years, 4 months ago

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