User Vincent Granville - Mathematics Stack Exchange

10 votes

Are there any series whose convergence is unknown?

answered Feb 9, 2020 at 22:40

6 votes

Potentially new approach to factoring big numbers

answered May 17, 2020 at 8:32

3 votes

Non standard solution to $f(x) = \frac{1}{2}\Big(f(\frac{x}{2}) + f(\frac{1+x}{2})\Big)$

answered Aug 22, 2019 at 17:01

3 votes

Successive records in mathematical sequences: surprising result

answered Aug 28, 2019 at 18:10

3 votes

Simple recurrences converging to $\log 2, \pi, e, \sqrt{2}$ and so on

answered Dec 31, 2019 at 18:26

2 votes

Integral $\int_0^\infty \frac{|\sin\sqrt{qx}|-|\sin\sqrt{px}|}{x}dx$

answered Apr 11, 2019 at 17:12

2 votes

Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

answered Aug 21, 2019 at 14:24

2 votes

Value of $\frac{1}{3!} - \frac{1}{6!} + \frac{1}{9!} - \frac{1}{12!} + \ldots$

answered Dec 23, 2019 at 0:41

1 vote

Potentially new approach to factoring big numbers

answered May 22, 2020 at 16:18

1 vote

Curious convergence domain for $x_n$ defined by $(a_1 n+ b_1) x_{n+2} = (a_2 n + b_2) x_{n+1} - (a_3 n + b_3) x_n$

answered Jan 4, 2020 at 21:19

1 vote

Derivative and calculus over sets such as the rational numbers

answered Dec 7, 2019 at 22:01

1 vote

Accepted

Density of a particular set of numbers

answered Dec 16, 2019 at 4:51

1 vote

Probability distribution of the product of random numbers

answered Nov 2, 2019 at 20:35

0 votes

Direct construction of the real numbers using only the integers (c.f. Eudoxus reals)

answered Sep 26, 2019 at 17:55

0 votes

The following seems true for a wide range of functions: $\sum_{k=1}^n f(k)f(n-k) = n f^2(n/2) (1 + o(1))$

answered Sep 29, 2019 at 19:33

0 votes

How can I prove that $4^{n} + 5$ is divisible by $3$.

answered Sep 29, 2019 at 17:26

0 votes

Limiting distributions (attractors) associated with the discrete difference operator - application to error detection

answered Nov 25, 2019 at 15:55

0 votes

Positiveness of some functions, connection with the central limit theorem and stable distributions

answered Nov 25, 2019 at 0:27

0 votes

Curious convergence domain for $x_n$ defined by $(a_1 n+ b_1) x_{n+2} = (a_2 n + b_2) x_{n+1} - (a_3 n + b_3) x_n$

answered Jan 5, 2020 at 18:33

0 votes

What is more elementary than: Introduction to Stochastic Processes by Lawler

answered Jul 8, 2018 at 21:11

0 votes

Accepted

Some distributions / auto-correlations associated with irrational numbers

answered Aug 15, 2019 at 14:41

0 votes

Accepted

Probability question with application to number theory and cryptography

answered Oct 15, 2020 at 0:40

0 votes

Interesting facts/ proofs about rational and irrational numbers

answered Jul 19, 2020 at 17:43

0 votes

Accepted

Conjecture about the distribution of $0/1$ in the binary expansion of rational numbers

answered Jan 22, 2020 at 8:26

0 votes

Accepted

Convergence and limit for Collatz type of recurrence

answered Feb 2, 2020 at 8:31

Stack Exchange Network

25 Answers

Are there any series whose convergence is unknown?

Potentially new approach to factoring big numbers

Non standard solution to $f(x) = \frac{1}{2}\Big(f(\frac{x}{2}) + f(\frac{1+x}{2})\Big)$

Successive records in mathematical sequences: surprising result

Simple recurrences converging to $\log 2, \pi, e, \sqrt{2}$ and so on

Integral $\int_0^\infty \frac{|\sin\sqrt{qx}|-|\sin\sqrt{px}|}{x}dx$

Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

Value of $\frac{1}{3!} - \frac{1}{6!} + \frac{1}{9!} - \frac{1}{12!} + \ldots$

Potentially new approach to factoring big numbers

Curious convergence domain for $x_n$ defined by $(a_1 n+ b_1) x_{n+2} = (a_2 n + b_2) x_{n+1} - (a_3 n + b_3) x_n$

Derivative and calculus over sets such as the rational numbers

Density of a particular set of numbers

Probability distribution of the product of random numbers

Direct construction of the real numbers using only the integers (c.f. Eudoxus reals)

The following seems true for a wide range of functions: $\sum_{k=1}^n f(k)f(n-k) = n f^2(n/2) (1 + o(1))$

How can I prove that $4^{n} + 5$ is divisible by $3$.

Limiting distributions (attractors) associated with the discrete difference operator - application to error detection

Positiveness of some functions, connection with the central limit theorem and stable distributions

Curious convergence domain for $x_n$ defined by $(a_1 n+ b_1) x_{n+2} = (a_2 n + b_2) x_{n+1} - (a_3 n + b_3) x_n$

What is more elementary than: Introduction to Stochastic Processes by Lawler

Some distributions / auto-correlations associated with irrational numbers

Probability question with application to number theory and cryptography

Interesting facts/ proofs about rational and irrational numbers

Conjecture about the distribution of $0/1$ in the binary expansion of rational numbers

Convergence and limit for Collatz type of recurrence