An "Egyptian fraction representation"  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
 On ternary Egyptian fractions with prime denominator, Florian Luca & Francesco Pappalardi, https://arxiv.org/pdf/1905.06151.pdf
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. :)
σ(T⊕V) = σT⊕σV
Definition of "Happy numbers" Show more
"A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits in base-ten, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers)." - https://en.wikipedia.org/wiki/Happy_number
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
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. https://www.monde-diplomatique.fr/2019/03/PUDAL/59625
I did not find any capitalist prime ≤ 10⁴ 😄, using the following code in SageMath Show more
assert is_prime(p), "imput must be prime"
classes = [(0, x) for x in range(1, p)]
factorial = 1
for j in range(2, p):
factorial *= j
factorial %= p
a, b = classes[factorial-1]
classes[factorial-1] = (a+1, b)
return sum(x for x, y in classes[:ceil((p-1)/100)]) >= (p-1)/2
A socialist prime  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 🙃
 Tim Trudgian, There are no socialist primes less than 10⁹, https://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 :
n! ≈ nⁿ · e⁻ⁿ · √(2πn)
PhD student in maths/computer science, curious in anything :).
Toots in English and occasionally en français.
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
\) for inline LaTeX, and
\] for display mode.