Integer as Sum of Polygonal Numbers/Historical Note/Fermat's Note

== Historical Note on Integer as Sum of Polygonal Numbers: 's Note in 's ==
 * Every positive integer is triangular or the sum of $2$ or $3$ triangular numbers; a square or the sum of $2$, $3$ or $4$ squares; a pentagonal number or the sum of $2$, $3$, $4$ or $5$ pentagonal numbers; and so on to infinity, whether it is a question of hexagonal, heptagonal or any polygonal numbers.


 * I cannot give the proof here, for it depends on many abstruse mysteries of numbers; but I intend to devote an entire book to this subject, and to present in this part of number theory astonishing advances beyond previously known boundaries.

No such book was ever written, although it is generally believed that he probably could have done so.