0
votes
0answers
15 views
Sequences satisfying gcd(S(x), S(y)) = S(gcd(x,y))
Consider the sequence S(x) = 2^x - 1. This sequence has two interesting properties:
a) If the GCD of S(x) and S(y) is S(gcd(x,y)), and
b) For any prime p, S(p-1) is divisible by …
0
votes
0answers
10 views
A question about time in Special and General Relativity.
I apologize if this question is considered too mathematically imprecise. My understanding of Special and
General Relativity comes from reading books which attempt to explain them t …
3
votes
2answers
266 views
In What Sense is Set Theory a ‘Foundation’ for Mathematics?
In what sense is set theory a foundation for mathematics? To my mind (for what that is worth), there are at least three (somewhat) distinct senses in which set 'theory' (I put "th …
0
votes
0answers
19 views
Smoothness and curvature of geodesics in a length space
Let $X$ be a nice compact subset of $R^d$. Given a function $p: X \to R^+$, define the length of a path $\gamma \subset X$ as $\ell(\gamma) = \int_\gamma p(x) dx$, and the distance …
2
votes
1answer
88 views
Groups with special automorphism group
I am looking for all finite groups $G$ such that for each subgroup $H$ of $G$ and each automorphism $\sigma$ of $H$ there exists an automorphism $\psi$ of $G$ whose restriction to …
0
votes
0answers
32 views
n balls, k colors, expected color change problem
I was asked this question during my interview recently and despite the amount of thinking i put into this, I am yet to figure it out:
Given $n$ balls which are painted by $k$ co …
-1
votes
0answers
57 views
if $f$ is a positive function such that $\int_0^\infty f$ converges, show that there is another function $g$ such that $\lim_{x \to \infty} \frac {g(x)} {f(x)} = \infty$ and $\int_0^\infty g$ also converges. [closed]
if $f$ is a positive function such that $\int_0^\infty f$ converges, show that there is another function $g$ such that $\lim_{x \to \infty} \frac {g(x)} {f(x)} = \infty$ and $\int_ …
0
votes
1answer
53 views
How is the expected fraction of zeros correctly calculated when throwing bits?
Here is a random sequence of 25 bits: 0101001100100011011010111
A sequence of any desired length can be obtained here
http://www.random.org/integers/?num=25&min=0&max=1& …
0
votes
2answers
81 views
open immersion between affine spaces
Let $j:\mathbb{A}^{n}\rightarrow\mathbb{A}^{n}$ an open immersion over a field $k$. Is it an isomorphism?
6
votes
1answer
126 views
Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?
Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers? Which of their properties and relations (e.g. usual trig ident …
0
votes
0answers
24 views
Best known asymptotically tight bound for the coupon subset collection problem?
For awhile I was under the impression that the rough asymptotic expression for the time to collect $m$ coupons from a set of $N$ unique elements was something like $E(T) \approx \T …
0
votes
0answers
22 views
Collages along composition of distributors
The construction of a collage of two categories $\bf A,B$ along a profunctor $\phi\colon \bf A\mid\hspace{-2mm}\to B$ gives a new category $\bf A \uplus_\phi B$ having as objects t …
0
votes
1answer
33 views
translating a given boolean function to universal boolean function
A Boolean function U($z_1$, $z_2$ ..... , $z_m$) is universal for given n > 1 if it realizes all Boolean functions f($x_l$ ..... $x_n$) by substituting for each $z_i$ with a variab …
2
votes
0answers
135 views
A technical question related to Zhang’s result of bounded prime gaps
Here is a link on the internet: https://www.dropbox.com/s/su3uak2a057yrqv/YitangZhang.pdf
Can someone teach me how to use trivial estimation to reach (6.1) on page 24? Namely, how …
2
votes
0answers
26 views
Elements of low multiplicative order and computing square roots modulo composites
In "On computing factors of cyclotomic polynomials", Richard P. Brent
gives the identity
$$ 4 \Phi_n(x) = A_n(x)^2 - (-1)^{(n-1)/2} n B_n(x)^2 \qquad (1) $$
where $n$ is odd squa …
