# 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): Entry:**Fermat's theorem** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Fermat's theorem**