User jlammy - Mathematics Stack Exchange

17 votes

1 answer

881 views

Strange point lies on common tangent of 9-point circle and incircle

asked Dec 31, 2017 at 19:34

15 votes

4 answers

2k views

Intuition behind picking group actions and Sylow

asked Feb 7, 2021 at 17:38

11 votes

1 answer

426 views

Find all functions on the non-zero reals to itself satisfying $f(xy)=f(x+y)(f(x)+f(y))$

asked Jul 31, 2016 at 13:49

10 votes

2 answers

564 views

Find all solutions to $f\left(x^2+xf(y)\right)=xf(x+y)$

asked Jul 22, 2016 at 18:42

9 votes

4 answers

3k views

Maximum area of triangle inside a convex polygon

asked Jul 18, 2016 at 21:06

9 votes

2 answers

605 views

$\frac{1}{n}\sum_{k=1}^n(X_k-\mathbb E[X_k])$ converges a.s. to $0$

asked Dec 28, 2020 at 21:37

8 votes

0 answers

265 views

Infinitely many primes divide some $\sum_{k=1}^n k!$

asked Apr 30, 2017 at 19:34

8 votes

5 answers

3k views

Maximum number of right-angled triangles

asked Apr 11, 2016 at 9:46

7 votes

1 answer

512 views

$m^2+2017=n^3$ has no solutions

asked Jul 20, 2016 at 22:36

6 votes

1 answer

206 views

$\lfloor x\rfloor \cdot \lfloor x^2\rfloor = \lfloor x^3\rfloor$ means that $x$ is close to an integer

asked Jul 14, 2016 at 17:13

6 votes

1 answer

477 views

(Non-continuous) solutions to $f\big(f(x)\big)=kx$ and $f\left(x^2\right)=xf(x)$

asked Jan 24, 2016 at 13:31

5 votes

3 answers

388 views

Smallest chain of consecutive integers not all coprime

asked Jul 13, 2016 at 20:33

5 votes

1 answer

101 views

Functions satisfying $f(x+f(y))=f(x+a)+y+b$

asked Oct 13, 2016 at 17:04

5 votes

0 answers

81 views

Choosing diagonals in an $n$-gon

asked Dec 31, 2017 at 19:17

4 votes

1 answer

201 views

Vertices connected by monochromatic paths in $K_{\underbrace{kn,\dots,kn}_{k~\text{times}}}$

asked May 7, 2017 at 20:38

4 votes

0 answers

75 views

Integer polynomials with $P(n)P(n+1)\in P(\mathbb Z)$

asked Sep 4, 2016 at 20:52

4 votes

1 answer

81 views

$\{\lfloor na\rfloor\mid n\in\mathbb N\}\cup\{\lfloor nb\rfloor\mid n\in\mathbb N\}$ is a permutation of $\mathbb N$ iff $ab=a+b$

asked Nov 6, 2016 at 14:15

4 votes

2 answers

249 views

Sum of distance to odd vertices = Sum of distance to even vertices in regular polygon

asked Dec 14, 2016 at 22:05

4 votes

1 answer

75 views

Induced subgraph is a trail of length $2r-1$

asked Mar 15, 2017 at 21:56

3 votes

1 answer

498 views

Perpendiculars and midpoints in orthocenter configuration

asked Feb 3, 2017 at 20:32

3 votes

1 answer

268 views

Area of quadrilateral build on the Napoleon's theorem figure

asked Mar 19, 2016 at 20:31

3 votes

1 answer

87 views

$x^n\{x^n\}<\frac{1}{4}$ for all $n\geq2016$ implies $x$ is an integer

asked Jul 29, 2016 at 21:13

2 votes

1 answer

271 views

Question about preserving cross ratios in projective geometry

asked Jul 16, 2016 at 12:36

2 votes

1 answer

115 views

Inequality on a sequence of $n$ reals whose sum is $0$

asked Jul 16, 2016 at 21:24

2 votes

2 answers

122 views

Equation with radicals and reciprocals

asked Jan 23, 2016 at 23:22

2 votes

1 answer

415 views

Inverse points concurrence on the circumcircle

asked May 27, 2016 at 18:59

2 votes

1 answer

279 views

$20-80-80$ triangle, rhombus with orthocenter, circumcenter

asked Jan 25, 2016 at 18:38

2 votes

0 answers

84 views

Infinitely many primes such that $x^x\equiv1\pmod p$ has more than $N$ solutions

asked Feb 5, 2017 at 23:07

2 votes

2 answers

666 views

Incenter lies on the Newton-Gauss line

asked Dec 20, 2016 at 19:07

2 votes

1 answer

215 views

No lattice point dominates another

asked Jan 14, 2017 at 16:22

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47 Questions

Strange point lies on common tangent of 9-point circle and incircle

Intuition behind picking group actions and Sylow

Find all functions on the non-zero reals to itself satisfying $f(xy)=f(x+y)(f(x)+f(y))$

Find all solutions to $f\left(x^2+xf(y)\right)=xf(x+y)$

Maximum area of triangle inside a convex polygon

$\frac{1}{n}\sum_{k=1}^n(X_k-\mathbb E[X_k])$ converges a.s. to $0$

Infinitely many primes divide some $\sum_{k=1}^n k!$

Maximum number of right-angled triangles

$m^2+2017=n^3$ has no solutions

$\lfloor x\rfloor \cdot \lfloor x^2\rfloor = \lfloor x^3\rfloor$ means that $x$ is close to an integer

(Non-continuous) solutions to $f\big(f(x)\big)=kx$ and $f\left(x^2\right)=xf(x)$

Smallest chain of consecutive integers not all coprime

Functions satisfying $f(x+f(y))=f(x+a)+y+b$

Choosing diagonals in an $n$-gon

Vertices connected by monochromatic paths in $K_{\underbrace{kn,\dots,kn}_{k~\text{times}}}$

Integer polynomials with $P(n)P(n+1)\in P(\mathbb Z)$

$\{\lfloor na\rfloor\mid n\in\mathbb N\}\cup\{\lfloor nb\rfloor\mid n\in\mathbb N\}$ is a permutation of $\mathbb N$ iff $ab=a+b$

Sum of distance to odd vertices = Sum of distance to even vertices in regular polygon

Induced subgraph is a trail of length $2r-1$

Perpendiculars and midpoints in orthocenter configuration

Area of quadrilateral build on the Napoleon's theorem figure

$x^n\{x^n\}<\frac{1}{4}$ for all $n\geq2016$ implies $x$ is an integer

Question about preserving cross ratios in projective geometry

Inequality on a sequence of $n$ reals whose sum is $0$

Equation with radicals and reciprocals

Inverse points concurrence on the circumcircle

$20-80-80$ triangle, rhombus with orthocenter, circumcenter

Infinitely many primes such that $x^x\equiv1\pmod p$ has more than $N$ solutions

Incenter lies on the Newton-Gauss line

No lattice point dominates another