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Consecutive power sum (Posted on 2021-05-12)

Find all positive integers n such that 3ⁿ+4ⁿ+...+(n+2)ⁿ=(n+3)ⁿ

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 8

The LHS is smaller for all values except 2 and 3

n=2: 3^2 + 4^2 = 5^2

n=3: 3^3 + 4^3 + 5^3 = 6^3

The ratio of RHS/LHS exceeds 1 for n>3 so there are no other solutions.

https://www.desmos.com/calculator/6nw8rxubj0

Posted by Jer on 2021-05-12 11:22:03

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