Are there any SpongeBob SquarePants experts here?

I would like to know from which episode are these images coming: vimeo.com/27806741.

It illustrates the "man in the middle" attack, a well-known attack in .

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Knowledge is knowing a tomato is a fruit. Wisdom is not putting it in a fruit salad. -- Miles Kington

Because this game will never be played enough (in my opinion), here is the trailer for Hollow Knight, my favorite game!

youtube.com/watch?v=UAO2urG23S

An "Egyptian fraction representation" [1] of a rational a/n ∈ ℚ is a solution in positive integers m₁, m₂, ..., mₖ∈ ℕ to the equation

a/n = 1/m₁ + 1/m₂ + ... + 1/mₖ

Example: 5/6 = 1/2 + 1/3

[1] On ternary Egyptian fractions with prime denominator, Florian Luca & Francesco Pappalardi, arxiv.org/pdf/1905.06151.pdf

SPOILER Avengers: endgame Show more

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Hi, I'm new here and I did not know here had a math community and I decided to join. I hope to share with all of you and learn new things from you. I speak Spanish and English. At this moment I study by my own mathematics. I love learning new things that I don't know. Nice to meet you, guys.

I've been on Mastodon for a time. That's the reason I created an account here to sharing mathematics topics with all of you. :)

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The graphs of cos(x) and tan(x) intersect at right angles - who knew ?!? More, have a look at the gradients - *very* interesting.

Definition of "Happy numbers" Show more

Definition of "Happy numbers" Show more

I am a big fan of the anime and manga , but until recently I did not read the webcomic, mainly because of the art.

Well, that was an error, this is way too hilarious.

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Though I will never take a notes with anything except paper and pencil, this is a great LaTeX figure tutorial, and now I'm playing with Inkscape

castel.dev/post/lecture-notes-

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Désormais en accès libre : depuis son accession à la présidence de la République, Emmanuel Macron a souvent assimilé les classes populaires à un groupe de fainéants incultes et braillards. monde-diplomatique.fr/2019/03/

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I did not find any capitalist prime ≤ 10⁴ 😄, using the following code in SageMath Show more

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So now I think I'll try to find "capitalist" primes: that I define as follow.

A capitalist prime is a prime number p > 5 such that at least 50% of the values 2!, 3!, ..., (p-1)! belong to at most 1% of the classes modulo p.

A socialist prime [1] is a prime number p > 5 such that 2!, 3!, ..., (p-1)! are all distinct modulo p.

It is called "socialist" because the values are equally distributed among the classes 🙃

[1] Tim Trudgian, There are no socialist primes less than 10⁹, arxiv.org/pdf/1310.6403.pdf

A friend told me that

n! ≤ nⁿ

was the only thing he could say about how fast factorials grow. Well, he's not that far, because we have Stirling's formula [1]:

n! ≈ nⁿ · e⁻ⁿ · √(2πn)

[1] en.wikipedia.org/wiki/Stirling

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