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Number Theory Level 5

What is the smallest positive integer expressible as the sum of the cubes of two different integers in two different ways?

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The answer is 91.

2 solutions

Anik Mandal
Feb 18, 2015

$\large{\boxed{1729}}$ is the smallest number expressible as the sum of the cubes of two $\textbf{positive}$ integers in two different ways.

But since in the question it has been asked with reference to $\textbf{integers}$ ,the least number in that case is $\large 91=6^{3}+(-5)^3=4^{3}+3^{3}$

If you allow for negative numbers, then you have to allow for a representation like $0 = 1^3 + (-1)^3 = 2^3 + (-2)^3$ .

Jon Haussmann - 6 years, 3 months ago

I have edited the question,sir.

Anik Mandal - 6 years, 3 months ago

I got the question right but can you please clarify that the number is positive. I tried 0 originally.

Sharky Kesa - 6 years, 3 months ago

Very nice question!!!!! Keep it up man!!!!!

Gagan Raj - 6 years, 3 months ago

Thanks for your compliment!!

Anik Mandal - 6 years, 3 months ago

Ramiel To-ong
Jun 5, 2015

same solution

This is a trap!

For more problems ,click here .

The answer is 91.

2 solutions

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