Fermat Theorem Combinatorics Proof

Правка en4, от Ashwanth.K, 2024-08-13 22:06:24

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 $$$a^{p-1} = 1 mod p$$$

References:
Wikepedia

История

 
 
 
 
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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'
en40 Английский Ashwanth.K 2024-08-14 07:10:21 47 Tiny change: 'ons. \n\n<spoiler' -> 'ons. \n![ ](https://ibb.co/DrMDhmJ)\n<spoiler'
en39 Английский Ashwanth.K 2024-08-14 00:55:29 258
en38 Английский Ashwanth.K 2024-08-14 00:51:19 0 Tiny change: ' characters are repea' -> ' character are repea' (published)
en37 Английский Ashwanth.K 2024-08-14 00:47:12 5 Tiny change: ' \n######References' -> ' \n##### References'
en36 Английский Ashwanth.K 2024-08-14 00:43:01 18
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'
en32 Английский Ashwanth.K 2024-08-14 00:09:51 866
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en29 Английский Ashwanth.K 2024-08-13 23:01:52 327 Tiny change: 'YYX, YXY \n- \n\n\nRefere' -> 'YYX, YXY \n\nRefere'
en28 Английский Ashwanth.K 2024-08-13 22:43:22 139
en27 Английский Ashwanth.K 2024-08-13 22:41:17 4 Tiny change: 'consider $A = 2, P = 3$ ' -> 'consider $a = 2, p = 3$ '
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en22 Английский Ashwanth.K 2024-08-13 22:28:39 416 Tiny change: ' $ = 2^4$ \n $ = 16$ ' -> ' $ = 2^4 = 16$ '
en21 Английский Ashwanth.K 2024-08-13 22:19:00 8 Tiny change: 'mple:\n Say a =' -> 'mple:\n Say a ='
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en18 Английский Ashwanth.K 2024-08-13 22:16:33 13 Tiny change: 'e Theorem:\n- States that' -> 'e Theorem: \n It states that'
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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\'
en8 Английский Ashwanth.K 2024-08-13 22:07:38 10
en7 Английский Ashwanth.K 2024-08-13 22:07:05 9 Tiny change: 'orem: \n &mdash; States th' -> 'orem: \n- States th'
en6 Английский Ashwanth.K 2024-08-13 22:06:55 0 Tiny change: 'rem: \n &mdash; States th' -> 'rem: \n - States th'
en5 Английский Ashwanth.K 2024-08-13 22:06:41 8 Tiny change: 'rem: \n States th' -> 'rem: \n - States th'
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en2 Английский Ashwanth.K 2024-08-13 22:04:27 287
en1 Английский Ashwanth.K 2024-08-13 22:00:23 307 Initial revision (saved to drafts)