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Cubic Summation divisibility (Posted on 2023-07-13)

For any positive integers n and m satisfying the equation n³+(n+1)³+(n+2)³=m³, prove that n+1 is divisible by 4.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

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The only solution to the equation is 3^3+4^3+5^3=6^3

n+1=4 which is divisible by 4.

I didn't prove this, but it's not an uncommon question.

https://math.stackexchange.com/questions/120254/sum-of-three-consecutive-cubes

Posted by Jer on 2023-07-14 18:52:01

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