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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
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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]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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
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
Newton's Sum
P162008   4
N 2 minutes ago by P162008
If $\sum_{cyc} a = 7, \sum_{cyc} a^2 = 15, \sum_{cyc} a^3 = 19$ and $\sum_{cyc} a^4 = 25$ where each summation runs over $4$ variables $a,b,c$ and $d.$ Then find the value of $\sum_{cyc} a^5.$
4 replies
P162008
Today at 1:51 AM
P162008
2 minutes ago
Inequalities
sqing   2
N 14 minutes ago by sqing
Let $ a,b \in [0 ,1] . $ Prove that
$$\frac{a}{ 1-ab+b }+\frac{b }{ 1-ab+a } \leq 2$$$$ \frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 }+\frac{ab }{2+ab }  \leq 1$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+ab  }\leq \frac{5}{2}$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+2ab  }\leq \frac{7}{3}$$$$\frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 } +\frac{ab }{1+ab }\leq \frac{7}{6 }$$
2 replies
sqing
5 hours ago
sqing
14 minutes ago
Inequalities
sqing   6
N 32 minutes ago by sqing
Let $ a,b,c $ be real numbers such that $ a^2+b^2+c^2=1. $ Prove that$$ |a-b|+|b-2c|+|c-3a|\leq 5$$$$|a-2b|+|b-3c|+|c-4a|\leq \sqrt{42}$$$$ |a-b|+|b-\frac{11}{10}c|+|c-a|\leq \frac{29}{10}$$
6 replies
1 viewing
sqing
Apr 22, 2025
sqing
32 minutes ago
2 var inequalities
sqing   1
N 35 minutes ago by sqing
Source: Own
Let $ a,b\geq 0 $ and $ a^2+b^2=1 . $ Prove that
$$ \frac{a}{ 1+ab+b }+\frac{b }{ 1+ab+a }+\frac{ab }{1+ ab }   \leq  1$$$$   \frac{a}{ 1+ab+b }+\frac{b }{ 1+ab+a }+\frac{ab }{\frac{1}{2}+ ab }\leq \frac{6\sqrt 2 }{7 }- \frac{1 }{14 } $$$$   \frac{a}{ 1+ab+b }+\frac{b }{ 1+ab+a }+\frac{ab }{1+\frac{1}{2} ab }\leq \frac{6(5\sqrt 2-1) }{35 }$$
1 reply
1 viewing
sqing
38 minutes ago
sqing
35 minutes ago
B.Math - geometry
mynamearzo   9
N 36 minutes ago by Apple_maths60
In a triangle $ABC$ , $D$ is a point on $BC$ such that $AD$ is the internal bisector of $\angle A$ . Now Suppose $\angle B$=$2\angle C$ and $CD=AB$ . Prove that $\angle A=72^0$.
9 replies
mynamearzo
Jun 17, 2012
Apple_maths60
36 minutes ago
Irrational equation
giangtruong13   5
N 39 minutes ago by pooh123
Solve the equation : $$(\sqrt{x}+1)[2-(x-6)\sqrt{x-3}]=x+8$$
5 replies
giangtruong13
Yesterday at 1:44 PM
pooh123
39 minutes ago
CHINA TST 2017 P6 DAY1
lingaguliguli   1
N 39 minutes ago by GreekIdiot
When i search the china TST 2017 problem 6 day I i crossed out this lemme, but don't know to prove it, anyone have suggestion? tks
Given a fixed number n, and a prime p. Let f(x)=(x+a_1)(x+a_2)...(x+a_n) in which a_1,a_2,...a_n are positive intergers. Show that there exist an interger M so that 0<v_p((f(M))< n + v_p(n!)
1 reply
lingaguliguli
Apr 23, 2025
GreekIdiot
39 minutes ago
Geometry inmo problem
Enes040612   2
N 41 minutes ago by Red_gear5246
Source: INMO 2008
Can anyone help with this problem? the book also starts the solution by saying IA1=IB1=IC1=2r which I'm not understanding why. The problem is at the attachments.
2 replies
Enes040612
Feb 13, 2025
Red_gear5246
41 minutes ago
Sharing My Solutions for IMO 2023 (All 6 Problems) – Feedback Welcome
Blackhole.LightKing   4
N 44 minutes ago by GreekIdiot
Hi everyone,

I worked through all six problems from the 2023 International Mathematical Olympiad (IMO 2023), and I would like to share my solutions here.

I tried to make the explanations clear and complete, and I also added diagrams for the geometry problems to make them easier to follow.

Topics covered:

Number Theory

Geometry

Algebra

Combinatorics

You can find the full solution PDF attached (or linked below).

https://agi-origin.ai/assets/pdf/AGI-Origin_IMO_2023_Solution.pdf

I’m still learning, so if you see any mistakes, unclear parts, or better ways to explain things, I would really appreciate your feedback!

Thank you for reading, and I hope this can be helpful to others who are studying IMO problems too
4 replies
Blackhole.LightKing
an hour ago
GreekIdiot
44 minutes ago
System of two diophantine equations
AlastorMoody   4
N an hour ago by MATHS_ENTUSIAST
Source: Balkan MO ShortList 2007 N1
Solve the given system in prime numbers
\begin{align*} x^2+yu = (x+u)^v \end{align*}\begin{align*} x^2+yz=u^4 \end{align*}
4 replies
AlastorMoody
Apr 6, 2020
MATHS_ENTUSIAST
an hour ago
A bash problem
kjhgyuio   1
N an hour ago by zhoujef000
........
1 reply
kjhgyuio
an hour ago
zhoujef000
an hour ago
Minimum term of n^m
Kunihiko_Chikaya   1
N an hour ago by Mathzeus1024
Source: 19?? Mie University entrance exam
For any two positive integers $ m,\ n\ (m\geq 2)$, suppose that $ n^m$ is expressed by the sum of $ n$ consecutive odd numbers. Express the minimum term in terms of $ n$ and $ m$.
1 reply
Kunihiko_Chikaya
Jan 28, 2010
Mathzeus1024
an hour ago
true or false ?
SunnyEvan   5
N an hour ago by SunnyEvan
Let $ a,b,c \geq 0 $ Prove that :
$$ \frac{3k}{k^4+k+1} \leq \frac{ka}{a+k^4b+kc}+\frac{kb}{b+k^4c+ka}+\frac{kc}{c+k^4a+kb} \leq k $$Where $ k \geq 1 $
5 replies
SunnyEvan
Apr 20, 2025
SunnyEvan
an hour ago
Inequalities
sqing   8
N an hour ago by sqing
Let $x,y\ge 0$ such that $ 13(x^3+y^3) \leq 125(1+xy)$. Prove that
$$  k(x+y)-xy\leq  5(2k-5)$$Where $k\geq 5.6797. $
$$  6(x+y)-xy\leq 35$$
8 replies
sqing
Apr 20, 2025
sqing
an hour ago
JEE Related ig?
mikkymini2   16
N Apr 18, 2025 by mikkymini2
Hey everyone,

Just wanted to see if there are any other JEE aspirants on this forum currently prepping for it[mention year if you can]

I am actually entering 10th this year and have decided to try for it...So this year is just going to go in me strengthening my math (IOQM level (heard its enough till Mains part, so will start from there) for the problem solving part, and learn some topics from 11th and 12th as well)

It would be great to connect with others who are going through the same thing - share study strategies, tips, resources, discuss, and maybe even form study groups(not sure how to tho :maybe: ) and motivate each other ig?. :D
So yea, cya later
16 replies
mikkymini2
Apr 10, 2025
mikkymini2
Apr 18, 2025
JEE Related ig?
G H J
G H BBookmark kLocked kLocked NReply
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mikkymini2
13 posts
#1
Y by
Hey everyone,

Just wanted to see if there are any other JEE aspirants on this forum currently prepping for it[mention year if you can]

I am actually entering 10th this year and have decided to try for it...So this year is just going to go in me strengthening my math (IOQM level (heard its enough till Mains part, so will start from there) for the problem solving part, and learn some topics from 11th and 12th as well)

It would be great to connect with others who are going through the same thing - share study strategies, tips, resources, discuss, and maybe even form study groups(not sure how to tho :maybe: ) and motivate each other ig?. :D
So yea, cya later
Z K Y
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SomeonecoolLovesMaths
3203 posts
#2
Y by
If someone creates such a forum or a thread then I will be eager to join.
Z K Y
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mikkymini2
13 posts
#3
Y by
Do share any forum or thread that you find that might be helpful :-D
Z K Y
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Idiot_of_the64squares
14 posts
#4
Y by
I am also in 10th and preparing for IOQM
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Idiot_of_the64squares
14 posts
#5
Y by
I am also looking for some peers to help in preparation, although I am not preparing for JEE now because my main aim is IOQM
This post has been edited 1 time. Last edited by Idiot_of_the64squares, Apr 11, 2025, 1:32 PM
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mikkymini2
13 posts
#6
Y by
Idiot_of_the64squares wrote:
I am also in 10th and preparing for IOQM

Thats great! :D Same here...my aim for now is IOQM as well! Btw you in ICSE or CBSE?
This post has been edited 1 time. Last edited by mikkymini2, Apr 11, 2025, 2:51 PM
Z K Y
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Idiot_of_the64squares
14 posts
#8
Y by
CBSE, what about you?
Z K Y
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mikkymini2
13 posts
#9
Y by
ICSE....
Z K Y
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Idiot_of_the64squares
14 posts
#10
Y by
How will you prepare, coaching or at Home?
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mikkymini2
13 posts
#11
Y by
For now at home with additional materials, you?
Z K Y
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Idiot_of_the64squares
14 posts
#12
Y by
I will also prepare at home
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momo.onthe.moon
1 post
#13
Y by
not jee but i want to prepare for ioqm, x as well
Z K Y
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Indianmathenthusiast1234
8 posts
#14
Y by
HEY IM PREPPING FOR BOTH
YALL WANNA CREATE A FORUM?
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Indianmathenthusiast1234
8 posts
#15
Y by
and IM ICSE TOO
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mikkymini2
13 posts
#16
Y by
Indianmathenthusiast1234 wrote:
HEY IM PREPPING FOR BOTH
YALL WANNA CREATE A FORUM?

Thats great! :D Not sure how to make a proper forum tho...
Z K Y
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Indianmathenthusiast1234
8 posts
#17
Y by
I've created a forum.
Its called Archimedes' Circle
Its public so anyone can join!
Please inform if someone's not bale to join! I'll be happy to help!
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mikkymini2
13 posts
#18
Y by
Found it!
Link for the others: https://artofproblemsolving.com/community/q1h3550945p34585423
This post has been edited 1 time. Last edited by mikkymini2, Apr 18, 2025, 7:52 AM
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