Fermat polygonal number theorem

The Fermat Polygonalzahlensatz is a mathematical theorem in number theory. He states that every natural number can be represented as a sum of at most - Eckszahlen. A well-known special case is the four- square theorem, which states that each number can be written as the sum of four square numbers. An example:

The Fermat Polygonalzahlensatz is named after Pierre de Fermat, comes from the following quote:

"I was the first who discovered the very beautiful and completely general theorem that every number is either a triangular number or the sum of two or three triangular numbers; any number or the sum of a square number of two, three or four squares is; either Fünfeckszahl or the sum of two, three, four or five pentagonal; and so on to infinity, regardless of whether it is a question of the hexagon, heptagon or any Polygonalzahlen. I can see the proof that depends on many and abstruse mysteries of numbers here do not specify; that's why I intend to dedicate this subject a whole book, and to provide arithmetic amazing progress over the previous known limits in this part. "

Joseph Louis Lagrange proved the special case of the four -squares theorem 1770 and Carl Friedrich Gauss in 1796 for the special case of triangular numbers. However, the evidence of the complete set was not until Augustin Louis Cauchy in 1813.