Fermat Theorem Combinatorics Proof

Правка en12, от ASHWANTH_K, 2024-08-13 22:09:27

Hello everyone,

I did like to give a brief overview of Fermat's theorem and its proof. There are various methods to prove Fermat's Little theorem, but I found the combinatorial approach to be the most straightforward and easy to understand. I'd like to discuss Fermat's theorem and its proof using combinatorics.

Fermat's Little Theorem:
- States that given 2 integers $$$a$$$ , $$$p$$$ where $$$a > 1$$$ and $$$p$$$ is a prime, It follows that $$$a^{p-1} \equiv 1 \pmod{p}$$$

References:
Wikepedia

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en42 Английский ASHWANTH_K 2024-08-14 07:15:35 6 Tiny change: ' \n\nThus, this comple' -> ' \n\nThis comple'
en41 Английский ASHWANTH_K 2024-08-14 07:15:05 110 Tiny change: 'ime and $a$ is any i' -> 'ime and $a > 1$ is any i'
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en35 Английский ASHWANTH_K 2024-08-14 00:40:07 33 Tiny change: ' \n\nReferenc' -> ' \n\nThus, completing the proof. \nReferenc'
en34 Английский ASHWANTH_K 2024-08-14 00:39:37 1091 Tiny change: 'xplanation and Proof">\nLet's ' -> 'xplanation">\nLet's '
en33 Английский ASHWANTH_K 2024-08-14 00:20:03 1135 Tiny change: 'inal form.`\n######Pr' -> 'inal form.\n######Pr'
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en12 Английский ASHWANTH_K 2024-08-13 22:09:27 2 Tiny change: 'v 1 \pmod{n}$ \n\n' -> 'v 1 \pmod{p}$ \n\n'
en11 Английский ASHWANTH_K 2024-08-13 22:09:16 11 Tiny change: ' \equiv 1 mod p$ \n\n\' -> ' \equiv 1 \pmod{n}$ \n\n\'
en10 Английский ASHWANTH_K 2024-08-13 22:08:23 8 Tiny change: ' $a^{p-1} = 1 mod ' -> ' $a^{p-1} \equiv 1 mod '
en9 Английский ASHWANTH_K 2024-08-13 22:07:51 4 Tiny change: '{p-1} = 1 mod p$ \n\' -> '{p-1} = 1 mod p$ \n\'
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en1 Английский ASHWANTH_K 2024-08-13 22:00:23 307 Initial revision (saved to drafts)