User Carolus - Mathematics Stack Exchange

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	1,065 reputation	bio	website		visits	member for	1 year, 11 months
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5

16

votes

1

answer

485

views

Why should a combinatorialist know category theory?

apr 7 at 16:32 Carolus 1,065

5

14

votes

2

answers

308

views

Solving the recurrence relation $a_n=\frac{a_{n-1}^2+a_{n-2}^2}{a_{n-1}+a_{n-2}}$

sequences-and-series recurrence-relations

nov 7 at 22:48 dexter04 1,132

1

13

votes

5

answers

879

views

How do we prove $n^n \mid m^m \Rightarrow n \mid m$?

elementary-number-theory

feb 17 at 20:24 Community♦ 1

1

12

votes

3

answers

249

views

Asymptotic formula for $\sum_{n \le x} \frac{\varphi(n)}{n^2}$

asymptotics analytic-number-theory

nov 9 '11 at 2:37 apatch 174

1

11

votes

2

answers

269

views

Find all positive integers $n$ for which $(n-1)!+1$ is a power of $n$

elementary-number-theory

dec 25 '11 at 4:54 Ehsan M. Kermani 3,334

1

8

votes

1

answer

282

views

A couple of formulas for $\pi$

sequences-and-series pi

nov 15 at 6:25 Carolus 1,065

6

votes

2

answers

170

views

Proving two sequences identical

number-theory sequences-and-series analytic-number-theory

may 15 at 16:04 Eric♦ 33.2k

6

votes

1

answer

130

views

Proof of $\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^n\frac{\sigma(k)}{k}=\zeta(2)$

number-theory

apr 18 '12 at 4:52 Jonas Kibelbek 3,627

6

votes

3

answers

149

views

How to generalize $\sigma_\alpha$ (Dirichlet convolution)

number-theory analytic-number-theory

jan 6 '12 at 17:55 Carolus 1,065

6

votes

3

answers

150

views

Showing $\pi(ax)/\pi(bx) \sim a/b$ as $x \to \infty$

number-theory prime-numbers analytic-number-theory

dec 5 '11 at 22:16 Captain Darling 379

1

5

votes

3

answers

350

views

Closed form formula for $\sum\limits_{k=1}^n k^k$

sequences-and-series exponentiation

jan 2 '12 at 5:04 marty cohen 6,298

5

votes

3

answers

228

views

How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?

elementary-number-theory

jul 27 '11 at 2:39 J. M. 38.9k

1

5

votes

5

answers

372

views

Proving two gcd's equal

elementary-number-theory

jul 19 '11 at 20:47 Community♦ 1

4

votes

2

answers

81

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Morphisms in a category with products

abstract-algebra category-theory

apr 30 at 20:20 Martin 3,688

2

4

votes

3

answers

147

views

What is the difference between analytic combinatorics and the theory of combinatorial species?

combinatorics soft-question category-theory asymptotics

apr 6 at 6:13 Qiaochu Yuan 117k

4

votes

1

answer

186

views

Asymptotics for sums of the form $\sum \limits_{\substack{1\leq k\leq n \\ (n,k)=1}}f(k)$

analytic-number-theory

nov 9 at 1:31 Eric♦ 33.2k

4

votes

2

answers

158

views

Integral related to $\sum\limits_{n=1}^\infty\sin^n(x)\cos^n(x)$

calculus integral

may 7 '12 at 12:39 J. M. 38.9k

4

votes

1

answer

103

views

Proof involving the logarithmic integral

special-functions analytic-number-theory

dec 3 '11 at 10:34 J. M. 38.9k

1

4

votes

2

answers

114

views

Equivalence of two relations involving $\pi(x)$ and $\vartheta(x)$

analytic-number-theory

dec 3 '11 at 8:33 Martin Sleziak 20.3k

1

3

votes

4

answers

381

views

$\sum\limits_{d \mid n} \mu(d) \omega(n/d)=0$ for composite numbers. How?

analytic-number-theory

may 9 at 7:12 Ethan 2,210

3

votes

2

answers

238

views

Inverse of completely multiplicative function(s)

number-theory analytic-number-theory

apr 13 at 18:14 Carolus 1,065

3

votes

0

answers

56

views

A proof concering $\Re(\log\zeta(\sigma+it))$

analytic-number-theory

jan 28 at 6:37 Carolus 1,065

1

3

votes

0

answers

136

views

Champernowne-like squares, are there any?

number-theory

dec 14 '11 at 16:29 J. M. 38.9k

3

votes

2

answers

119

views

Showing $\log \frac{x^x}{x!}=O(x)$

asymptotics

dec 5 '11 at 10:09 Bruno 6,971

3

votes

1

answer

168

views

Proving a polynomial $f(x)$ composite for infinitely many $x$

elementary-number-theory polynomials

nov 27 '11 at 11:55 Gerry Myerson 85.7k

2

votes

2

answers

60

views

Justifying $\sum\limits_{n\leq x}d(n)=\sum\limits_{a\leq x}\left[\frac{x}{a}\right]$

number-theory

dec 10 at 15:47 Cantor 502

2

votes

1

answer

105

views

Adjoining an element to a ring

abstract-algebra ring-theory

nov 22 at 16:45 ineff 2,273

2

votes

1

answer

30

views

Help with a proof concerning ideals

abstract-algebra ring-theory ideals

nov 20 at 9:34 Berci 20.6k

2

votes

2

answers

205

views

Proving convergence of a recursively defined sequence

sequences-and-series recurrence-relations

nov 3 at 20:11 André Nicolas 160k

2

votes

1

answer

125

views

Asymptotic formula of $\sum_{n \le x} \frac{d(n)}{n^a}$

asymptotics analytic-number-theory

nov 6 '11 at 5:29 Carolus 1,065

Carolus

40 Questions