Post #870390
2026-03-28 02:35 UTC
Replies (12)
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@shayman@cosocial.ca 2026-03-28 02:49
Informal proof that for a prime p >=5, p²-1 must be a multiple of 24. p²-1 = (p-1)(p+1) p-1, p, p+1 are three consecutive integers. One of them must be divisible by 3 - and it can't be p, because p is prime. So either p-1 or p+1 is a multiple of 3. Also, p is odd, so p-1 and p+1 are both even - and one or the other must be divisible by 4. One is a multiple of 2, the other of 4. So the product of p-1 and p+1 has factors of 2, 3 and 4, and must be a multiple of 2*3*4 =24.
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@Starfia@mastodon.social 2026-03-28 02:37
@shayman@cosocial.ca – Wow!
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@GeePawHill@mastodon.social 2026-03-28 04:21
@shayman@cosocial.ca Okay. Yes. That's very fucking cool, actually.
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@brandonscript@appdot.net 2026-03-28 06:07
@shayman@cosocial.ca ok this is cool. But also.. what is the meaning of it? It must have some sort of existential value to math or at least life or the simulation or... something?
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@kauer@aus.social 2026-03-28 06:55
@shayman@cosocial.ca Soooo is it also true that for any prime number >= 3, p squared - 1 is divisible by 8?
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@funbaker@chaos.social 2026-03-28 08:45
@shayman@cosocial.ca b...but I thought 42 is the answer to everything?
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@Devonkiwi@mastodonapp.uk 2026-03-28 08:46
@shayman@cosocial.ca Mind. Blown.
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@pewterbaw@mastodon.scot 2026-03-28 11:22
@shayman@cosocial.ca really?!?!
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@TeaDrivenDev@metalhead.club 2026-03-28 14:54
@shayman@cosocial.ca For some reason, I find this scary. What special right does 24 have to do that?
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@arrakeen_urbanite@universeodon.com 2026-03-28 18:48
@shayman@cosocial.ca What sorcery is this‽
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@philip@mastodon.mallegolhansen.com 2026-03-29 00:04
@shayman@cosocial.ca Quite
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@hellman@mathstodon.xyz 2026-03-29 18:57
@shayman@cosocial.ca 240 | (p^4-1) for primes p >= 7 504 | (p^6-1) for primes p >= 11 480 | (p^8-1) for primes p >= 7 264 | (p^10-1) for primes p >= 13 65520 | (p^12-1) for primes p >= 17 ... See https://oeis.org/A006863