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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 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
UC Berkeley Integration Bee 2025 Bracket Rounds
Silver08   16
N 6 minutes ago by quasar_lord
Regular Round

Quarterfinals

Semifinals

3rd Place Match

Finals
16 replies
1 viewing
Silver08
May 9, 2025
quasar_lord
6 minutes ago
Set Partition
Butterfly   0
an hour ago
For the set of positive integers $\{1,2,…,n\}(n\ge 3)$, no matter how its elements are partitioned into two subsets, at least one of the subsets must contain three numbers $a,b,c$ ($a=b$ is allowed) such that $ab=c$. Find the minimal $n$.
0 replies
Butterfly
an hour ago
0 replies
Points Lying on its Cevian Triangle's Thomson Cubic
Feuerbach-Gergonne   1
N 2 hours ago by golue3120
Source: Own
Given $\triangle ABC$ and a point $P$, let $\triangle DEF$ be the cevian triangle of $P$ with respect to $\triangle ABC$. Let $H$ be the orthocenter of $\triangle ABC$, and denote the isotomic conjugate of $H, P$ with respect to $\triangle ABC$ by $X, Q$, respectively. Let the centroid of $\triangle DEF$ be $M$, and denote the isogonal conjugate of $P$ with respect to $\triangle DEF$ by $R$. Prove that
$$
P, Q, X \text{ are collinear} \iff P, R, M \text{ are collinear}. 
$$or in brief
$$
P \in \text{ K007 of } \triangle ABC \iff P \in \text{ K002 of } \triangle DEF. 
$$
1 reply
Feuerbach-Gergonne
Jul 19, 2024
golue3120
2 hours ago
Areas of triangles AOH, BOH, COH
Arne   71
N 2 hours ago by EpicBird08
Source: APMO 2004, Problem 2
Let $O$ be the circumcenter and $H$ the orthocenter of an acute triangle $ABC$. Prove that the area of one of the triangles $AOH$, $BOH$ and $COH$ is equal to the sum of the areas of the other two.
71 replies
Arne
Mar 23, 2004
EpicBird08
2 hours ago
Problem 6
termas   68
N 2 hours ago by HamstPan38825
Source: IMO 2016
There are $n\ge 2$ line segments in the plane such that every two segments cross and no three segments meet at a point. Geoff has to choose an endpoint of each segment and place a frog on it facing the other endpoint. Then he will clap his hands $n-1$ times. Every time he claps,each frog will immediately jump forward to the next intersection point on its segment. Frogs never change the direction of their jumps. Geoff wishes to place the frogs in such a way that no two of them will ever occupy the same intersection point at the same time.

(a) Prove that Geoff can always fulfill his wish if $n$ is odd.

(b) Prove that Geoff can never fulfill his wish if $n$ is even.
68 replies
termas
Jul 12, 2016
HamstPan38825
2 hours ago
2n^2+4n-1 and 3n+4 have common powers
bin_sherlo   2
N 3 hours ago by Assassino9931
Source: Türkiye 2025 JBMO TST P5
Find all positive integers $n$ such that a positive integer power of $2n^2+4n-1$ equals to a positive integer power of $3n+4$.
2 replies
bin_sherlo
Yesterday at 7:13 PM
Assassino9931
3 hours ago
combi/nt
blug   2
N 3 hours ago by aaravdodhia
Prove that every positive integer $n$ can be written in the form
$$n=a_1+a_2+...+a_k,$$where $a_m=2^i3^j$ for some non-negative $i, j$ such that
$$a_x\nmid a_y$$for every $x, y\leq k$.
2 replies
blug
May 9, 2025
aaravdodhia
3 hours ago
System of equations in juniors' exam
AlperenINAN   2
N 3 hours ago by Assassino9931
Source: Turkey JBMO TST 2025 P3
Find all positive real solutions $(a, b, c)$ to the following system:
$$
\begin{aligned}
a^2 + \frac{b}{a} &= 8, \\
ab + c^2 &= 18, \\
3a + b + c &= 9\sqrt{3}.
\end{aligned}
$$
2 replies
AlperenINAN
Yesterday at 7:41 PM
Assassino9931
3 hours ago
Trigo relation in a right angled. ISIBS2011P10
Sayan   10
N 3 hours ago by mqoi_KOLA
Show that the triangle whose angles satisfy the equality
\[\frac{\sin^2A+\sin^2B+\sin^2C}{\cos^2A+\cos^2B+\cos^2C} = 2\]
is right angled.
10 replies
Sayan
Mar 31, 2013
mqoi_KOLA
3 hours ago
Triangle is similar to two others
gghx   3
N 3 hours ago by LeYohan
Source: SMO junior 2024 Q2
Let $ABCD$ be a parallelogram and points $E,F$ be on its exterior. If triangles $BCF$ and $DEC$ are similar, i.e. $\triangle BCF \sim \triangle DEC$, prove that triangle $AEF$ is similar to these two triangles.
3 replies
gghx
Oct 12, 2024
LeYohan
3 hours ago
Parallel lines lead to similar triangles
a1267ab   30
N 3 hours ago by Ilikeminecraft
Source: USA TST for EGMO 2020, Problem 2, by Andrew Gu
Let $ABC$ be a triangle and let $P$ be a point not lying on any of the three lines $AB$, $BC$, or $CA$. Distinct points $D$, $E$, and $F$ lie on lines $BC$, $AC$, and $AB$, respectively, such that $\overline{DE}\parallel \overline{CP}$ and $\overline{DF}\parallel \overline{BP}$. Show that there exists a point $Q$ on the circumcircle of $\triangle AEF$ such that $\triangle BAQ$ is similar to $\triangle PAC$.

Andrew Gu
30 replies
a1267ab
Dec 16, 2019
Ilikeminecraft
3 hours ago
ISI UGB 2025 P3
SomeonecoolLovesMaths   8
N 3 hours ago by mqoi_KOLA
Source: ISI UGB 2025 P3
Suppose $f : [0,1] \longrightarrow \mathbb{R}$ is differentiable with $f(0) = 0$. If $|f'(x) | \leq f(x)$ for all $x \in [0,1]$, then show that $f(x) = 0$ for all $x$.
8 replies
SomeonecoolLovesMaths
Yesterday at 11:32 AM
mqoi_KOLA
3 hours ago
Minimum value
Martin.s   3
N Yesterday at 5:24 PM by Martin.s
What is the minimum value of
$$
\frac{|a + b + c + d| \left( |a - b| |b - c| |c - d| + |b - a| |c - a| |d - a| \right)}{|a - b| |b - c| |c - d| |d - a|}
$$over all triples $a, b, c, d$ of distinct real numbers such that
$a^2 + b^2 + c^2 + d^2 = 3(ab + bc + cd + da).$

3 replies
Martin.s
Oct 17, 2024
Martin.s
Yesterday at 5:24 PM
Cost Question
bassamali01   9
N Yesterday at 4:19 PM by Juno_34
Sorry, I have been struggling with this question so much. It is a simple derivative question as I think it is. Can I get some help on it?
9 replies
bassamali01
Dec 7, 2017
Juno_34
Yesterday at 4:19 PM
Inegration stuff, integration bee
Acumlus   8
N Apr 11, 2025 by Silver08
I want to learn how to integrate, I'm a ms student with knowledge about math counts ,amc 10 even tho that want help mebut I don't want to dwell in calc, I just want to learn how to integrate and nothing else like I don't want to study it deep, how can I learn how to integrate its for an integration bee hosted near me its a state uni and I want to join so in the span of 2 months how can I learn to integrate without learning calc like fully
8 replies
Acumlus
Apr 7, 2025
Silver08
Apr 11, 2025
Inegration stuff, integration bee
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Acumlus
17 posts
#1
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I want to learn how to integrate, I'm a ms student with knowledge about math counts ,amc 10 even tho that want help mebut I don't want to dwell in calc, I just want to learn how to integrate and nothing else like I don't want to study it deep, how can I learn how to integrate its for an integration bee hosted near me its a state uni and I want to join so in the span of 2 months how can I learn to integrate without learning calc like fully
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paxtonw
35 posts
#2
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Do you understand differentiation? You most likely won't be able to understand intergration without first understanding differentiation.
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snake2020
4510 posts
#3
Y by
"Acumlus"
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Acumlus
17 posts
#4
Y by
paxtonw wrote:
Do you understand differentiation? You most likely won't be able to understand intergration without first understanding differentiation.

ill try to learn differentiation, how should I approach this like learning how to integrate
Z K Y
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Acumlus
17 posts
#5
Y by
snake2020 wrote:
"Acumlus"

it was a typo, don't mind the you know what part
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paxtonw
35 posts
#6
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Acumlus wrote:
paxtonw wrote:
Do you understand differentiation? You most likely won't be able to understand intergration without first understanding differentiation.

ill try to learn differentiation, how should I approach this like learning how to integrate

Khan Acedamty
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Acumlus
17 posts
#7
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thx , bump
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HacheB2031
394 posts
#8
Y by
You should learn differentiation because:
1. Differentiation is easier than indefinite integration.
2. It has many interesting properties, particularly extrema and MVT.
3. The Fundamental Theorem of Calculus links differentiation and integration.
4. Most integration tricks rely on differentiation because of derivative rules.
Try to learn how to differentiate first.
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Silver08
461 posts
#9 • 1 Y
Y by paxtonw
You should definitely learn differentiation first!!

1. Learn the concept of Differentiation rules!! Watch from this Youtube Channel: PatrickJMT
2. Practice differentiation with example problems!! Watch from this Youtube Channel: OrganicChemistryTutor
After that, apply the same procedure for integral concepts: learn first from PatrickJMT, then practice problems from OrganicChemistryTutor.

Then after all that, once your confident and comfortable enough....you can join the dark side :evilgrin:
I have an "integration bee training" series on Youtube which is easy to find, and I made a book for Integration Bee Problem Writers:
https://artofproblemsolving.com/community/c1967976h3218725

I wish you the best of luck!!!
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