Editing Fermat polygonal number theorem (section)

{{short description|Every positive integer is a sum of at most n n-gonal numbers}}
{{distinguish|Fermat's Last Theorem}}

In [[additive number theory]], the '''Fermat polygonal number theorem''' states that every positive integer is a sum of at most {{mvar|n}} [[Polygonal number|{{mvar|n}}-gonal number]]s. That is, every positive integer can be written as the sum of three or fewer [[triangular number]]s, and as the sum of four or fewer [[square number]]s, and as the sum of five or fewer [[pentagonal number]]s, and so on. That is, the {{mvar|n}}-gonal numbers form an [[additive basis]] of order {{mvar|n}}.