Fermat's Polygonal Number Theorem

Fermat's Polygonal Number Theorem states that every positive integer is a sum of at most n numbers of the n-gonal kind, meaning every positive integer can be written as the sum of three or fewer triangular numbers, four or fewer square numbers, five or fewer pentagonal numbers, and so on for every polygon size. In the language of additive number theory, the n-gonal numbers form an additive basis of order n.