perfect numbers
Fermat [ edit ] Pierre de Fermat Pierre de Fermat (1607–1665) never published his writings; in particular, his work on number theory is contained almost entirely in letters to mathematicians and in private marginal notes. [36] In his notes and letters, he scarcely wrote any proofs - he had no models in the area. [37] Over his lifetime, Fermat made the following contributions to the field: One of Fermat's first interests was perfect numbers (which appear in Euclid, Elements IX) and amicable numbers ; [note 7] these topics led him to work on integer divisors , which were from the beginning among the subjects of the correspondence (1636 onwards) that put him in touch with the mathematical community of the day. [38] In 1638, Fermat claimed, without proof, that all whole numbers can be expressed as the sum of four squares or fewer. [39] Fermat's little theorem (1640): [40] if a is not divisible by a prime...