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Site Support Tech support and questions about AoPS classes and materials
Tech support and questions about AoPS classes and materials
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k a August Highlights and 2025 AoPS Online Class Information
jwelsh   0
Yesterday at 2:14 PM
CONGRATULATIONS to all the competitors at this year’s International Mathematical Olympiad (IMO)! The US Team took second place with 5 gold medals and 1 silver - we are proud to say that each member of the 2025 IMO team has participated in an AoPS WOOT (Worldwide Online Olympiad Training) class!

"As a parent, I'm deeply grateful to AoPS. Tiger has taken very few math courses outside of AoPS, except for a local Math Circle that doesn't focus on Olympiad math. AoPS has been one of the most important resources in his journey. Without AoPS, Tiger wouldn't be where he is today — especially considering he's grown up in a family with no STEM background at all."
— Doreen Dai, parent of IMO US Team Member Tiger Zhang

Interested to learn more about our WOOT programs? Check out the course page here or join a Free Scheduled Info Session. Early bird pricing ends August 19th!:
CodeWOOT Code Jam - Monday, August 11th
ChemWOOT Chemistry Jam - Wednesday, August 13th
PhysicsWOOT Physics Jam - Thursday, August 14th
MathWOOT Math Jam - Friday, August 15th

There is still time to enroll in our last wave of summer camps that start in August at the Virtual Campus, our video-based platform, for math and language arts! From Math Beasts Camp 6 (Prealgebra Prep) to AMC 10/12 Prep, you can find an informative 2-week camp before school starts. Plus, our math camps don’t have homework and cover cool enrichment topics like graph theory. Our language arts courses will build the foundation for next year’s challenges, such as Language Arts Triathlon for levels 5-6 and Academic Essay Writing for high school students.

Lastly, Fall is right around the corner! You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US. We’ve opened new Academy locations in San Mateo, CA, Pasadena, CA, Saratoga, CA, Johns Creek, GA, Northbrook, IL, and Upper West Side (NYC), New York.

Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
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Prealgebra 2 Self-Paced

Prealgebra 2
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Introduction to Algebra A Self-Paced

Introduction to Algebra A
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Introduction to Counting & Probability Self-Paced

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Introduction to Number Theory
Wednesday, Aug 13 - Oct 29
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Introduction to Algebra B
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Paradoxes and Infinity
Sat & Sun, Sep 13 - Sep 14 (1:00 - 4:00 PM PT/4:00 - 7:00 PM ET)

Intermediate: Grades 8-12

Intermediate Algebra
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Precalculus
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Calculus
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Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
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F=ma Problem Series
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Visit the pages linked for full schedule details for each of these programs!


MathWOOT Level 1
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Introduction to Physics
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Physics 1: Mechanics
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0 replies
jwelsh
Yesterday at 2:14 PM
0 replies
Posting LaTeX
siamchung_degree   5
N 2 hours ago by ahxun2006
I want to give a post with LaTeX codes, but when I press submit, it says that new users are not allowed to post images in the Community.
5 replies
siamchung_degree
3 hours ago
ahxun2006
2 hours ago
AoPS randomly capitalizing tags
ajovanovic   15
N 3 hours ago by skronkmonster
Sometimes, when I create a new post on my forum and add a tag, the tag's first letter automatically capitalizes the first letter! What is causing this, and is there a way to stop it?
15 replies
ajovanovic
Jul 29, 2025
skronkmonster
3 hours ago
help me out here
the_mathtrovert_next_door   4
N 3 hours ago by melloncandy
I want to make a forum, how can i do that, AoPS wiki is not helping me
4 replies
the_mathtrovert_next_door
Today at 7:41 AM
melloncandy
3 hours ago
Number theory problem
littleduckysteve   4
N 4 hours ago by littleduckysteve
A number in base 16 has 2025 digits, and no letters in its representation. The sum of the digits in this number is greater than 10126. How many such numbers are there, if the base 10 representation is a palindrome.
4 replies
littleduckysteve
Yesterday at 2:55 PM
littleduckysteve
4 hours ago
Inequalities
sqing   15
N 5 hours ago by sqing
Let $ a,b \geq 0, 2a  +b^2=1   . $ Prove that
$$ \frac{\sqrt{a+b}}{a(b+1)}   \geq \sqrt{2} $$Let $ a,b \geq 0, a^2 +2b^2 =2  . $ Prove that
$$ \frac{\sqrt{a+2b}}{a(b+1)}   \geq \frac{9}{8\sqrt{2}} $$Let $ a,b \geq 0, 2a^2 +b^2 =1  . $ Prove that
$$\dfrac{a^2}{a+b}\leq\frac{1}{\sqrt{2}} $$$$ \frac{7}{10}>\frac{a+b}{a^2+b^2+1} \geq\frac{\sqrt{2}}{3} $$
15 replies
sqing
Jul 31, 2025
sqing
5 hours ago
Inequalities
sqing   14
N 5 hours ago by sqing
Let $ a,b \geq 0,a +b =1 . $ Prove that
$$ \sqrt{a^4 + \frac{3}{4}ab} + \sqrt{b^4 + \frac{3}{4}ab} \geq 1$$Let $ a,b \geq 0,a +b =4 . $ Prove that
$$ \sqrt{a^4 + 12ab} + \sqrt{b^4 + 12ab} \geq 16$$Let $ a,b,c \geq 0,a +b +c=1 . $ Prove that
$$  a^2 + b^2 + c^2 + \frac{1}{2}\sqrt{3abc}  \geq \frac{1}{2}$$Let $ a,b,c \geq 0,a +b +c=3 . $ Prove that
$$  a^2 + b^2 + c^2 +\frac{3}{2} \sqrt{abc}  \geq \frac{9}{2}$$
14 replies
sqing
Yesterday at 12:19 PM
sqing
5 hours ago
Help me please
Hahahsafdk3l   6
N Today at 11:02 AM by Pal702004
Let \( (x_n) \) be a sequence defined by
\[
x_1 = 2,\quad x_2 = 7,\quad x_{n+2} = 4x_{n+1} - x_n \quad \text{for all } n \ge 1.
\]Prove that no term of the sequence is a perfect square.
6 replies
Hahahsafdk3l
Yesterday at 7:27 AM
Pal702004
Today at 11:02 AM
USAMO problem
littleduckysteve   0
Today at 10:45 AM
A finite set $S$ of positive integers has the property that, for each $s \in S$, and each positive integer divisor $d$ of $s$, there exists a unique element $t \in S$ Satisfying $gcd$$(s,t) = d$. (The elements $s$ and $t$ could be equal.) Given this information, find all possible values for the number of elements of $S$.
0 replies
littleduckysteve
Today at 10:45 AM
0 replies
Find the value of angle C
markosa   16
N Today at 10:29 AM by littleduckysteve
Given a triangle ABC with base BC

angle B = 3x
angle C = x
AP is the bisector of base BC (i.e.) BP = PC
angle APB = 45 degrees

Find x

I know there are multiple methods to solve this problem using cosine law, coord geo
But is there any pure geometrical solution?
16 replies
markosa
Jul 25, 2025
littleduckysteve
Today at 10:29 AM
Prove that this is a multiple of 3
littleduckysteve   2
N Today at 10:25 AM by littleduckysteve
Prove or disprove that $2^a+(-1)^{a+1}$ is a multiple of 3 for $a \geq 0$.
2 replies
littleduckysteve
Today at 9:01 AM
littleduckysteve
Today at 10:25 AM
2017 preRMO p16, 5 distinct 2-digit numbers in a geometric progression
parmenides51   7
N Today at 8:29 AM by littleduckysteve
Five distinct $2$-digit numbers are in a geometric progression. Find the middle term.
7 replies
parmenides51
Aug 9, 2019
littleduckysteve
Today at 8:29 AM
Perfect Numbers
the_mathtrovert_next_door   0
Today at 8:05 AM
Ok, so we have the conjecture "there are infinitely many perfect numbers". so , i thought about looking at this from a algebraic perspective , so i made a function $$f(x)=\sigma(x)-2x$$where the $\sigma(x)$ function is the sum of divisors of x, now i decided to use a closed form expression for $\sigma(x)$. i used $$\sigma(x)=\sum_{i=1}^{\lceil x \rceil} i\cdot \lfloor cos^2 ( \frac{\pi \cdot x}{i} ) \rfloor$$. The cosine part detects whether i divides x, if it does, it evaluates to 1 and you get i, if not, it evaluates to zero. if we just plugged it back in the original function , we get, $$ f(x)= -2x+\sum_{i=1}^{\lceil x \rceil} i\cdot \lfloor cos^2 ( \frac{\pi \cdot x}{i} ) \rfloor$$. Since this function uses floors, its domain is all reals, now if we plug a non integer in , we get $f(x)=-2x$, so only integers are roots , so if we can prove that there are infinitely many roots, we are done, so a thing to notice is that there are infinitely many places where this function is greater that zero(abundant numbers ) and infinitely many places where it is less that 0(deficient numbers), so i tried using that here , but no go, thought someone would like to see this.
0 replies
the_mathtrovert_next_door
Today at 8:05 AM
0 replies
Sphere problem
littleduckysteve   0
Today at 7:58 AM
Suppose that there are two concentric spheres with radii, 6 and 10 respectively. 2 more spheres are drawn such that they are externally tangent to each other and the sphere of radius 6 and internally tangent to the sphere of radius 10. Another sphere is tangent to both of these spheres and is tangent to the sphere of radius 10. Find the difference between the greatest possible radius of this sphere and the least possible radius of this sphere.

answer

hint 1

hint 2

hint 3
0 replies
littleduckysteve
Today at 7:58 AM
0 replies
Favicon Not Loading In Classroom
nosassy0   2
N Yesterday at 10:18 PM by LoreleiA
In my classroom (I am specifically taking 4210 Calculus) the favicon isn't loading. Developer tools says the server is throwing a 404 error. This obviously isn't a big deal but I thought I'd let someone know because I'd much rather have the happy AoPS cube than the generic world symbol. Thanks guys!
2 replies
nosassy0
Jul 26, 2025
LoreleiA
Yesterday at 10:18 PM
k Python turtle
Speedysolver1   15
N Apr 16, 2025 by jlacosta
It gave a turtle window as seen without import turtle
print("this does not import turtle")

IMAGE
15 replies
Speedysolver1
Apr 10, 2025
jlacosta
Apr 16, 2025
Python turtle
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G H BBookmark kLocked kLocked NReply
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Speedysolver1
143 posts
#1
Y by
It gave a turtle window as seen without import turtle
  1. print("this does not import turtle")

https://cdn.artofproblemsolving.com/attachments/5/d/89ec62e714378f19a06d77f2a6931d1d342dcd.png
This post has been edited 3 times. Last edited by Speedysolver1, Apr 10, 2025, 8:28 PM
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Speedysolver1
143 posts
#2
Y by
Also it doesn’t print
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Irreplaceable
1297 posts
#4
Y by
Speedysolver1 wrote:
It gave a turtle window as seen without import turtle
  1. print("this does not import turtle")
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Irreplaceable
1297 posts
#5
Y by
I fixed it you should check your keyboard if it is on INT or US
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Demetri
1646 posts
#6 • 1 Y
Y by Irreplaceable
It doesn't print because you are using tildas(`) around the string (why are you using tildas) and it imports turtle because that is how aops code is desgined. @2above fixes it for you
This post has been edited 3 times. Last edited by Demetri, Apr 10, 2025, 8:11 PM
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Speedysolver1
143 posts
#7
Y by
I edited can reproduce
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Craftybutterfly
593 posts
#8
Y by
Try doing print('your words'). notice that I used ' instead of ". Or maybe there is something wrong with AoPS python window
This post has been edited 1 time. Last edited by Craftybutterfly, Apr 10, 2025, 8:26 PM
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Irreplaceable
1297 posts
#9
Y by
Craftybutterfly wrote:
Try doing print('your words'). notice that I used ' instead of "

no no you can use single quotes for a print statement
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Demetri
1646 posts
#10
Y by
I edited can reproduce
The issue is resolved? It prints now, and importing turtle is intended, in fact its in the code:
if (prog.indexOf("import turtle") > -1) {
            $('#' + Sk.TurtleGraphics.target).show();
Z Y
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Speedysolver1
143 posts
#11
Y by
Demetri wrote:
I edited can reproduce
The issue is resolved? It prints now, and importing turtle is intended, in fact its in the code:
if (prog.indexOf("import turtle") > -1) {
            $('#' + Sk.TurtleGraphics.target).show();

not resolved it still happens
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Speedysolver1
143 posts
#12
Y by
see the attachments
Attachments:
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Demetri
1646 posts
#13
Y by
Demetri wrote:
I edited can reproduce
The issue is resolved? It prints now, and importing turtle is intended, in fact its in the code:
if (prog.indexOf("import turtle") > -1) {
            $('#' + Sk.TurtleGraphics.target).show();

not resolved it still happens
It is resolved, it happens on purpose.
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Speedysolver1
143 posts
#14
Y by
Why does it
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Demetri
1646 posts
#15 • 2 Y
Y by Speedysolver1, InsightfulHawk16
Why does it
Aops searches for "import turtle" in the python code and if it detects that it will import it. @below you can put [RESOLVED] in the title because \req lock doesn't do much
This post has been edited 1 time. Last edited by Demetri, Apr 10, 2025, 8:43 PM
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bpan2021
2728 posts
#18 • 1 Y
Y by Speedysolver1
Why does it
Aops searches for "import turtle" in the python code and if it detects that it will import it. @below you can put [RESOLVED] in the title because \req lock doesn't do much

But that is not how Python is supposed to function. It's only supposed to register instances where "import turtle" is not some string, another data type, or is part of some piece of code that doesn't want to import turtle, but rather an actual import statement. If "import turtle" was not in the code as an import statement, then the turtle box should not appear.

The way that this functions is wrong and isn't accepted in Python, so it should be a bug.
This post has been edited 1 time. Last edited by bpan2021, Apr 11, 2025, 12:41 AM
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jlacosta
678 posts
#24 • 1 Y
Y by aidan0626
Thanks for reporting this! We'll pass it along.
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