Fermat polygonal number theorem
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Every positive integer is a sum of at most <math>n<math> <math>n<math>-polygonal numbers.
An example would be 17 = 10 + 6 + 1
A well-known special case of this is Lagrange's four-square theorem
For example, 7 = 4 + 1 + 1 + 1
Jacobi proved the square case in 1772 and Gauss proved the triangular case in 1796, but the theorem was not resolved until it was finally proven by Cauchy in 1813.
References
- Eric W. Weisstein. "Fermat's Polygonal Number Theorem." From MathWorld--A Wolfram Web Resource (http://mathworld.wolfram.com). http://mathworld.wolfram.com/FermatsPolygonalNumberTheorem.html
See Also
External links
- Fermat's Polygonal Number Theorem -- fram MathWorld (http://mathworld.wolfram.com/FermatsPolygonalNumberTheorem.html)