Fermat's Little Theorem/Historical Note
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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