User kerzol

24 votes

2 answers

2k views

Why "One cannot construct more than countably many independent random variables"?

asked Jul 25, 2014 at 7:58

7 votes

2 answers

742 views

How to prove that the polynomial $x^n+x^{n-1} +⋯+x^2+x−1$ is irreducible over $ \mathbb Q$?

asked Apr 28, 2021 at 21:42

5 votes

1 answer

262 views

Galois group of the polynomial $x^n+x^{n-1} +⋯+x^2+x−1$

asked May 3, 2021 at 14:00

3 votes

0 answers

359 views

Does the Min-max theorem hold in the case of primitive matrices?

asked Mar 10, 2016 at 9:31

2 votes

1 answer

69 views

Suppose that $0 \le f(n) \le 1$, why $\lim_{n \to \infty} (1 - f(n))^n = 0 \iff \lim_{n \to \infty} f(n)n = \infty$?

asked Oct 31, 2013 at 16:34

1 vote

2 answers

109 views

How to solve these functional equations $f(x) = 1 + f(x) + f(x^2) + \ldots $ and $f(x) = 1 + f(x) + \big(f(x^2)\big)^2 + \ldots $?

asked Jul 2, 2017 at 14:44

1 vote

1 answer

92 views

How to solve $F(z,q) = q + z F(z,q) + z^2 \big( F(z,q^2) \big)^2$?

asked Jul 4, 2017 at 8:33

0 votes

0 answers

46 views

What can we say about the closed-form solutions of $ x^q - 2x + 1$ for $\def\N{\mathbb{N}} q \in \N^+$?

asked Apr 27, 2021 at 20:56

0 votes

0 answers

32 views

Reference request for the generating function $\frac{x^k}{1-x-x^2-\cdots-x^k-x^{k+1}}$ of generalized $k$-step Fibonacci numbers

asked Oct 27, 2021 at 13:27

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9 Questions

Why "One cannot construct more than countably many independent random variables"?

How to prove that the polynomial $x^n+x^{n-1} +⋯+x^2+x−1$ is irreducible over $ \mathbb Q$?

Galois group of the polynomial $x^n+x^{n-1} +⋯+x^2+x−1$

Does the Min-max theorem hold in the case of primitive matrices?

Suppose that $0 \le f(n) \le 1$, why $\lim_{n \to \infty} (1 - f(n))^n = 0 \iff \lim_{n \to \infty} f(n)n = \infty$?

How to solve these functional equations $f(x) = 1 + f(x) + f(x^2) + \ldots $ and $f(x) = 1 + f(x) + \big(f(x^2)\big)^2 + \ldots $?

How to solve $F(z,q) = q + z F(z,q) + z^2 \big( F(z,q^2) \big)^2$?

What can we say about the closed-form solutions of $ x^q - 2x + 1$ for $\def\N{\mathbb{N}} q \in \N^+$?

Reference request for the generating function $\frac{x^k}{1-x-x^2-\cdots-x^k-x^{k+1}}$ of generalized $k$-step Fibonacci numbers