\(f(k) = \sum_{r=1}^{n} r^k\). Find an integer \(x\) that solves the equation \(f(x) = \bigl(f(1)\bigr)^2\).
Thursday, December 16, 2010
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Credit
This is an original puzzle from cotpi.
Further reading
The following is a list of resources on related topics:
- Weisstein, Eric W. "Triangular Number." Wolfram MathWorld. 29 Aug. 2011. Wolfram Research. 9 Sep. 2011 <http://mathworld.wolfram.com/TriangularNumber.html>.
- Weisstein, Eric W. "Nicomachus's Theorem." Wolfram MathWorld. 29 Aug. 2011. Wolfram Research. 9 Sep. 2011 <http://mathworld.wolfram.com/NicomachussTheorem.html>.
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Prunthaban Kanthakumar solved this puzzle:
\(3\) from what I learnt in school.