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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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

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0 replies
jlacosta
Apr 2, 2025
0 replies
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
J
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Feet of perpendiculars to diagonal in cyclic quadrilateral
jl_   2
N 27 minutes ago by lw202277
Source: Malaysia IMONST 2 2023 (Primary) P6
Suppose $ABCD$ is a cyclic quadrilateral with $\angle ABC = \angle ADC = 90^{\circ}$. Let $E$ and $F$ be the feet of perpendiculars from $A$ and $C$ to $BD$ respectively. Prove that $BE = DF$.
2 replies
1 viewing
jl_
3 hours ago
lw202277
27 minutes ago
J
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The old one is gone.
EeEeRUT   9
N 30 minutes ago by Jupiterballs
Source: EGMO 2025 P2
An infinite increasing sequence $a_1 < a_2 < a_3 < \cdots$ of positive integers is called central if for every positive integer $n$ , the arithmetic mean of the first $a_n$ terms of the sequence is equal to $a_n$.

Show that there exists an infinite sequence $b_1, b_2, b_3, \dots$ of positive integers such that for every central sequence $a_1, a_2, a_3, \dots, $ there are infinitely many positive integers $n$ with $a_n = b_n$.
9 replies
EeEeRUT
Apr 16, 2025
Jupiterballs
30 minutes ago
J
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Inequalities
Humberto_Filho   2
N 30 minutes ago by damyan
Source: From the material : A brief introduction to inequalities.
Let a,b be nonnegative real numbers such that $a + b \leq 2$. Prove that :

$$(1+a^2)(1+b^2) \geq (1 + (\frac{a+b}{2})^2)^2$$
2 replies
1 viewing
Humberto_Filho
Apr 12, 2023
damyan
30 minutes ago
J
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Error in forum
Speedysolver1   1
N 36 minutes ago by Demetri
Will put video
1 reply
Speedysolver1
an hour ago
Demetri
36 minutes ago
J
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3 var inequalities
sqing   1
N 37 minutes ago by sqing
Source: Own
Let $ a,b> 0 $ and $ a+b\leq 2ab . $ Prove that
$$ \frac{ a + b }{ a^2(1+ b^2)} \leq\frac{1 }{\sqrt 2}-\frac{1 }{2}$$$$ \frac{ a +ab+ b }{ a^2(1+ b^2)} \leq \sqrt 2-1$$$$ \frac{ a +a^2b^2+ b }{ a^2(1+ b^2)} \leq\frac{\sqrt5 }{2}$$
1 reply
sqing
43 minutes ago
sqing
37 minutes ago
J
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Divisibility holds for all naturals
XbenX   13
N 43 minutes ago by zRevenant
Source: 2018 Balkan MO Shortlist N5
Let $x,y$ be positive integers. If for each positive integer $n$ we have that $$(ny)^2+1\mid x^{\varphi(n)}-1.$$Prove that $x=1$.

(Silouanos Brazitikos, Greece)
13 replies
XbenX
May 22, 2019
zRevenant
43 minutes ago
J
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Sum and product of 5 numbers
jl_   1
N an hour ago by jl_
Source: Malaysia IMONST 2 2023 (Primary) P2
Ivan bought $50$ cats consisting of five different breeds. He records the number of cats of each breed and after multiplying these five numbers he obtains the number $100000$. How many cats of each breed does he have?
1 reply
jl_
4 hours ago
jl_
an hour ago
J
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Interesting inequalities
sqing   3
N an hour ago by sqing
Source: Own
Let $ a,b> 0 $ and $ a+b\leq 2ab . $ Prove that
$$\frac{ 9a^2- ab +9b^2 }{ a^2(1+b^4)}\leq\frac{17 }{2}$$$$\frac{a- ab+b }{ a^2(1+b^4)}\leq\frac{1 }{2}$$$$\frac{2a- 3ab+2b }{ a^2(1+b^4)}\leq\frac{1 }{2}$$
3 replies
sqing
5 hours ago
sqing
an hour ago
J
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a+b+c=2 ine
KhuongTrang   30
N an hour ago by KhuongTrang
Source: own
Problem. Given non-negative real numbers $a,b,c: ab+bc+ca>0$ satisfying $a+b+c=2.$ Prove that $$\color{blue}{\frac{a}{\sqrt{2a+3bc}}+\frac{b}{\sqrt{2b+3ca}}+\frac{c}{\sqrt{2c+3ab}} \le \sqrt{\frac{2}{ab+bc+ca}}. }$$
30 replies
KhuongTrang
Jun 25, 2024
KhuongTrang
an hour ago
J
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Introducing myself at AoPS, and what's your magic wand?
asuth_asuth   937
N an hour ago by PikaPika999
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.
937 replies
asuth_asuth
Mar 30, 2025
PikaPika999
an hour ago
J
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2021 EGMO P1: {m, 2m+1, 3m} is fantabulous
anser   55
N 2 hours ago by NicoN9
Source: 2021 EGMO P1
The number 2021 is fantabulous. For any positive integer $m$, if any element of the set $\{m, 2m+1, 3m\}$ is fantabulous, then all the elements are fantabulous. Does it follow that the number $2021^{2021}$ is fantabulous?
55 replies
anser
Apr 13, 2021
NicoN9
2 hours ago
J
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Complicated FE
XAN4   0
2 hours ago
Source: own
Find all solutions for the functional equation $f(xyz)+\sum_{cyc}f(\frac{yz}x)=f(x)\cdot f(y)\cdot f(z)$, in which $f$: $\mathbb R^+\rightarrow\mathbb R^+$
Note: the solution is actually quite obvious - $f(x)=x^n+\frac1{x^n}$, but the proof is important.
Note 2: it is likely that the result can be generalized into a more advanced questions, potentially involving more bash.
0 replies
XAN4
2 hours ago
0 replies
J
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k Alcumus Error
AtlantisHSK2   4
N Yesterday at 8:25 PM by jlacosta
Hi I've been doing pre 2 (I'm almost done), however I am having a problem with the alcumus that is integrated into the program. I have finished these alcumus sections well over 3 times, but after a few days they display that they're unfinished, I was wondering whether this was a bug and if there is some way to fix it.
4 replies
AtlantisHSK2
Yesterday at 7:36 PM
jlacosta
Yesterday at 8:25 PM
J
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k help me PLEASE
dwead   4
N Yesterday at 6:29 PM by jlacosta
Im wondering if there is any way to reset progress in a specific subject in alcumus like algebra or geometry the reason i want to do that is because im getting progress when im not even doing them and it's kinda annoying when i have to skip the ones that ive done but really haven't
4 replies
dwead
Yesterday at 12:12 PM
jlacosta
Yesterday at 6:29 PM
J
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J
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k Two submit buttons?
Craftybutterfly   6
N Apr 3, 2025 by Craftybutterfly
Summary of the problem: on phones, there are two submit response buttons
Page URL: any topic
Steps to reproduce:
1.open a topic
2. press reply
3.you see it
...
Expected behavior: there’s supposed to be one submit button
Frequency: 100%
Operating system(s): iPhone XR
Browser(s), including version: chrome latest version
Additional information: https://drive.google.com/file/d/1kFakLeI1aXoPAQHAwhVneXLWg6OaCaCv/view?usp=drivesdk
6 replies
Craftybutterfly
Apr 3, 2025
Craftybutterfly
Apr 3, 2025
J
Two submit buttons?
G H J
Reveal topic tags
posts
reply
submit
phone
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Craftybutterfly
387 posts
Craftybutterfly
#1 h  Apr 3, 2025, 12:49 AM
Y by
Summary of the problem: on phones, there are two submit response buttons
Page URL: any topic
Steps to reproduce:
1.open a topic
2. press reply
3.you see it
...
Expected behavior: there’s supposed to be one submit button
Frequency: 100%
Operating system(s): iPhone XR
Browser(s), including version: chrome latest version
Additional information: https://drive.google.com/file/d/1kFakLeI1aXoPAQHAwhVneXLWg6OaCaCv/view?usp=drivesdk
Attachments:
This post has been edited 2 times. Last edited by Craftybutterfly, Apr 3, 2025, 5:03 AM
Reason: e
Z Y
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bpan2021
2614 posts
bpan2021
#2 h  Apr 3, 2025, 2:04 AM
Y by
I can see this as well, but I believe it's intended behavior so mobile users can interact with the site more efficiently.
Z Y
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Craftybutterfly
387 posts
Craftybutterfly
#3 h  Apr 3, 2025, 3:11 AM
Y by
But it shows up no matter what so they technically don’t need to do anything except press submit
Z Y
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k1glaucus
669 posts
k1glaucus
#4 h  Apr 3, 2025, 11:51 AM
Y by
its always like that on mobile i think its fine
Z Y
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Craftybutterfly
387 posts
Craftybutterfly
#5 h  Apr 3, 2025, 3:08 PM
Y by
Why is it not like that on computer then?
Z Y
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k1glaucus
669 posts
k1glaucus
#6 h  Apr 3, 2025, 3:10 PM
Y by
because with the computer you dont need the submit button to be lower, but it can be useful on mobile because its closer to the keyboard ig?
Z Y
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Craftybutterfly
387 posts
Craftybutterfly
#7 h  Apr 3, 2025, 3:11 PM
Y by
That does not make sense.
Z Y
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