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Introducing myself at AoPS, and what's your magic wand?
asuth_asuth 708
N
by zhenghua
Hi!
I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.
Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops
I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.
I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.
Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops
I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.
708 replies
Distribution of prime numbers
Rainbow1971 3
N
by Rainbow1971
Could anybody possibly prove that the limit of 
is 
, maybe even with rather elementary means? As usual, 
denotes the 
-th prime number. The problem of that limit came up in my partial solution of this problem: https://artofproblemsolving.com/community/c7h3495516.
Thank you for your efforts.
is 
, maybe even with rather elementary means? As usual, 
denotes the 
-th prime number. The problem of that limit came up in my partial solution of this problem: https://artofproblemsolving.com/community/c7h3495516.Thank you for your efforts.
3 replies
limsup a_n/n^4
EthanWYX2009 3
N
by loup blanc
Source: 2023 Aug taca-15
Let 
. Define 
as the average of all 
for 
. Determine the value of ![\[ a = \lim_{k \to \infty} \sup_{n \geq k} \frac{a_n}{n^4} .\]](//latex.artofproblemsolving.com/5/2/d/52d93af7aafa6657689246d9a74c8eb05d96efa3.png)
. Define 
as the average of all 
for 
. Determine the value of ![\[ a = \lim_{k \to \infty} \sup_{n \geq k} \frac{a_n}{n^4} .\]](http://latex.artofproblemsolving.com/5/2/d/52d93af7aafa6657689246d9a74c8eb05d96efa3.png)
3 replies
Chebyshev polynomial and prime number
mofidy 2
N
by mofidy
Let 
be a Chebyshev polynomial of the second kind. If n>2 and x > 2 is a integer, Could 
be a prime number?
Thanks.
be a Chebyshev polynomial of the second kind. If n>2 and x > 2 is a integer, Could 
be a prime number?Thanks.
2 replies
Romanian National Olympiad 2024 - Grade 11 - Problem 1
Filipjack 4
N
by Fibonacci_math
Source: Romanian National Olympiad 2024 - Grade 11 - Problem 1
Let 
be an open interval and 
a twice differentiable function such that 
for any 
Prove that 
for any
be an open interval and 
a twice differentiable function such that 
for any 
Prove that 
for any
4 replies
Romania NMO 2023 Grade 11 P1
DanDumitrescu 14
N
by Rohit-2006
Source: Romania National Olympiad 2023
Determine twice differentiable functions 
which verify relation
![\[
\left( f'(x) \right)^2 + f''(x) \leq 0, \forall x \in \mathbb{R}.
\]](//latex.artofproblemsolving.com/3/a/2/3a235e8be4c61c32f376999e61d64973db21dc75.png)
which verify relation![\[
\left( f'(x) \right)^2 + f''(x) \leq 0, \forall x \in \mathbb{R}.
\]](http://latex.artofproblemsolving.com/3/a/2/3a235e8be4c61c32f376999e61d64973db21dc75.png)
14 replies
f(x)<=f(a) for all a and all x in a left neighbour of a implies monotony if cont
CatalinBordea 7
N
by solyaris
Source: Romanian District Olympiad 2012, Grade XI, Problem 4
A function 
has property 
if for any real number 
there exists a 
such that 
for all 
a) Give an example of a function with property
that is not monotone on 
b) Prove that a continuous function that has property is nondecreasing.
has property 
if for any real number 
there exists a 
such that 
for all 
a) Give an example of a function with property
that is not monotone on 
b) Prove that a continuous function that has property
is nondecreasing.
7 replies
vectorspace
We2592 1
N
by Acridian9
Q.) Let 
where
is field. Define addition of elements of 
coordinate wise and for 
and 
define 
.
Is is a vector space over field
how to solve it please help
where
is field. Define addition of elements of 
coordinate wise and for 
and 
define 
.Is
is a vector space over field how to solve it please help
1 reply
Rigid sets of points
a_507_bc 3
N
by solyaris
Source: ICMC 8.1 P6
A set of points in the plane is called rigid if each point is equidistant from the three (or more) points nearest to it.
(a) Does there exist a rigid set of
points?
(b) Does there exist a rigid set of
points?
(a) Does there exist a rigid set of
points?(b) Does there exist a rigid set of
points?
3 replies
Finding pairs of functions of class C^2 with a certain property
Ciobi_ 3
N
by solyaris
Source: Romania NMO 2025 11.1
Find all pairs of twice differentiable functions 
, with their second derivative being continuous, such that the following holds for all 
: ![\[(f(x)-g(y))(f'(x)-g'(y))(f''(x)-g''(y))=0\]](//latex.artofproblemsolving.com/0/2/9/029a935e28ca0a9b36e65702689cca91eeb8f614.png)
, with their second derivative being continuous, such that the following holds for all 
: ![\[(f(x)-g(y))(f'(x)-g'(y))(f''(x)-g''(y))=0\]](http://latex.artofproblemsolving.com/0/2/9/029a935e28ca0a9b36e65702689cca91eeb8f614.png)
3 replies
