Fermat's Little Theorem/Historical Note

Historical Note on Fermat's Little Theorem

Fermat's Little Theorem was first stated, without proof, by Pierre de Fermat in $1640$.

Chinese mathematicians were aware of the result for $n = 2$ some $2500$ years ago.

The appearance of the first published proof of this result is the subject of differing opinions.

Some sources have it that the first published proof was by Leonhard Paul Euler $1736$.

Others state that it was first proved by Gottfried Wilhelm von Leibniz in an undated manuscript, and that he may have known a proof before $1688$, perhaps as early as $1683$.

MathWorld's page on the subject reports the first published proof as being by Leonhard Paul Euler $1749$, but it is possible this has been conflated with the proof for Fermat's Two Squares Theorem.

Sources

• 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs
• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.13$: Fermat ($\text {1601}$ – $\text {1665}$)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Fermat's theorem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Fermat's theorem