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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
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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
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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
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UC Berkeley Integration Bee 2025 Bracket Rounds
Silver08   63
N 4 minutes ago by quasar_lord
Regular Round

Quarterfinals

Semifinals

3rd Place Match

Finals
63 replies
Silver08
May 9, 2025
quasar_lord
4 minutes ago
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Tough integral
Martin.s   1
N 23 minutes ago by Martin.s
$$\int_0^{\pi/2}\ln(\tan(\theta/2)) \;\frac{4\cos\theta\cos(2\theta)}{4\sin^4\theta+1}\,d\theta.$$
1 reply
Martin.s
May 12, 2025
Martin.s
23 minutes ago
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Concurrency of tangent touchpoint lines on thales circles
MathMystic33   2
N an hour ago by Diamond-jumper76
Source: 2024 Macedonian Team Selection Test P4
Let $\triangle ABC$ be an acute scalene triangle. Denote by $k_A$ the circle with diameter $BC$, and let $B_A,C_A$ be the contact points of the tangents from $A$ to $k_A$, chosen so that $B$ and $B_A$ lie on opposite sides of $AC$ and $C$ and $C_A$ lie on opposite sides of $AB$. Similarly, let $k_B$ be the circle with diameter $CA$, with tangents from $B$ touching at $C_B,A_B$, and $k_C$ the circle with diameter $AB$, with tangents from $C$ touching at $A_C,B_C$.
Prove that the lines $B_AC_A, C_BA_B, A_CB_C$ are concurrent.
2 replies
MathMystic33
Yesterday at 7:41 PM
Diamond-jumper76
an hour ago
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Find all possible values of q-p
yunxiu   18
N an hour ago by Jupiterballs
Source: 2012 European Girls’ Mathematical Olympiad P5
The numbers $p$ and $q$ are prime and satisfy
\[\frac{p}{{p + 1}} + \frac{{q + 1}}{q} = \frac{{2n}}{{n + 2}}\]
for some positive integer $n$. Find all possible values of $q-p$.

Luxembourg (Pierre Haas)
18 replies
yunxiu
Apr 13, 2012
Jupiterballs
an hour ago
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Inspired by nhathhuyyp5c
sqing   3
N an hour ago by sqing
Source: Own
Let $ x,y>0, x+2y- 3xy\leq 4. $Prove that
$$ \frac{1}{x^2} + 2y^2 + 3x + \frac{4}{y} \geq 3\left(2+\sqrt[3]{\frac{9}{4} }\right)$$
3 replies
sqing
3 hours ago
sqing
an hour ago
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Easy but Nice 12
TelvCohl   1
N an hour ago by Luis González
Source: Own
Given a $ \triangle ABC $ with orthocenter $ H $ and a point $ P $ lying on the Euler line of $ \triangle ABC. $ Prove that the midpoint of $ PH $ lies on the Thomson cubic of the pedal triangle of $ P $ WRT $ \triangle ABC. $
1 reply
TelvCohl
Mar 8, 2025
Luis González
an hour ago
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Similar Problems
Saucepan_man02   2
N an hour ago by quasar_lord
Could anyone post some problems which are similar to the below problem:

Find the real solution of: $$x^9+9/8 x^6+27/64 x^3-x+219/512.$$
Sol(outline)
2 replies
Saucepan_man02
May 12, 2025
quasar_lord
an hour ago
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Inspired by old results
sqing   0
an hour ago
Source: Own
Let $ a,b,c>0 $ . Prove that
$$\frac{a+kb}{b+c}+\frac{b+kc}{c+a}+\frac{c+ka}{a+b}\geq \frac{3(k+1)}{2}$$W here $-1 \leq k \leq \frac{537}{90}.$
0 replies
sqing
an hour ago
0 replies
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orthocenter on sus circle
DVDTSB   2
N 2 hours ago by Diamond-jumper76
Source: Romania TST 2025 Day 2 P1
Let \( ABC \) be an acute triangle with \( AB < AC \), and let \( O \) be the center of its circumcircle. Let \( A' \) be the reflection of \( A \) with respect to \( BC \). The line through \( O \) parallel to \( BC \) intersects \( AC \) at \( F \), and the tangent at \( F \) to the circle \( \odot(BFC) \) intersects the line through \( A' \) parallel to \( BC \) at point \( M \). Let \( K \) be a point on the ray \( AB \), starting at \( A \), such that \( AK = 4AB \).
Show that the orthocenter of triangle \( ABC \) lies on the circle with diameter \( KM \).

Proposed by Radu Lecoiu

2 replies
DVDTSB
Yesterday at 12:18 PM
Diamond-jumper76
2 hours ago
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problem 5
termas   74
N 2 hours ago by maromex
Source: IMO 2016
The equation
$$(x-1)(x-2)\cdots(x-2016)=(x-1)(x-2)\cdots (x-2016)$$is written on the board, with $2016$ linear factors on each side. What is the least possible value of $k$ for which it is possible to erase exactly $k$ of these $4032$ linear factors so that at least one factor remains on each side and the resulting equation has no real solutions?
74 replies
termas
Jul 12, 2016
maromex
2 hours ago
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I think I know why this problem was rejected by IMO PSC several times...
mshtand1   1
N 2 hours ago by sarjinius
Source: Ukrainian Mathematical Olympiad 2025. Day 2, Problem 11.8
Exactly $102$ country leaders arrived at the IMO. At the final session, the IMO chairperson wants to introduce some changes to the regulations, which the leaders must approve. To pass the changes, the chairperson must gather at least \(\frac{2}{3}\) of the votes "FOR" out of the total number of leaders. Some leaders do not attend such meetings, and it is known that there will be exactly $81$ leaders present. The chairperson must seat them in a square-shaped conference hall of size \(9 \times 9\), where each leader will be seated in a designated \(1 \times 1\) cell. It is known that exactly $28$ of these $81$ leaders will surely support the chairperson, i.e., they will always vote "FOR." All others will vote as follows: At the last second of voting, they will look at how their neighbors voted up to that moment — neighbors are defined as leaders seated in adjacent cells \(1 \times 1\) (sharing a side). If the majority of neighbors voted "FOR," they will also vote "FOR." If there is no such majority, they will vote "AGAINST." For example, a leader seated in a corner of the hall has exactly $2$ neighbors and will vote "FOR" only if both of their neighbors voted "FOR."

(a) Can the IMO chairperson arrange their $28$ supporters so that they vote "FOR" in the first second of voting and thereby secure a "FOR" vote from at least \(\frac{2}{3}\) of all $102$ leaders?

(b) What is the maximum number of "FOR" votes the chairperson can obtain by seating their 28 supporters appropriately?

Proposed by Bogdan Rublov
1 reply
mshtand1
Mar 14, 2025
sarjinius
2 hours ago
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Quadrilateral with Congruent Diagonals
v_Enhance   38
N 3 hours ago by Giant_PT
Source: USA TSTST 2012, Problem 2
Let $ABCD$ be a quadrilateral with $AC = BD$. Diagonals $AC$ and $BD$ meet at $P$. Let $\omega_1$ and $O_1$ denote the circumcircle and the circumcenter of triangle $ABP$. Let $\omega_2$ and $O_2$ denote the circumcircle and circumcenter of triangle $CDP$. Segment $BC$ meets $\omega_1$ and $\omega_2$ again at $S$ and $T$ (other than $B$ and $C$), respectively. Let $M$ and $N$ be the midpoints of minor arcs $\widehat {SP}$ (not including $B$) and $\widehat {TP}$ (not including $C$). Prove that $MN \parallel O_1O_2$.
38 replies
v_Enhance
Jul 19, 2012
Giant_PT
3 hours ago
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Prove the statement
Butterfly   2
N 4 hours ago by Gauler
Given an infinite sequence $\{x_n\} \subseteq [0,1]$, there exists some constant $C$, for any $r>0$, among the sequence $x_n$ and $x_m$ could be chosen to satisfy $|n-m|\ge r $ and $|x_n-x_m|<\frac{C}{|n-m|}$.
2 replies
Butterfly
May 7, 2025
Gauler
4 hours ago
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UMich Math
missionsqhc   0
Yesterday at 4:31 PM
I was recently accepted into the University of Michigan as a math major. If anyone studies math at UMich or knows anything about the program, could you share your experience? How would you rate the program? I know UMich is well-regarded for math (among many other things) but from my understanding, it is not quite at the level of an MIT or CalTech. What math programs is it comparable to? How does the rigor of the curricula compare to other top math programs? What are the other students like—is there a thriving contest math community? How accessible are research opportunities and graduate-level classes? Are most students looking to get into pure math and become research mathematicians or are most people focused on applied fields?

Also, aside from the math program, how is UMich overall? What were the advantages and disadvantages from being at such a large school? I was admitted to the Residential College (RC) within the College of Literature, Science, and the Arts. This is supposed to emulate a liberal arts college (while still allowing me access to the resources of a major research university). Could anyone speak on the RC?

How academically-inclined are UMich students? I’ve heard the school is big on sports and school spirit. I am just concerned that there may be a lot of subpar in-state students. How is the climate of Ann Arbor and how is the city in general?

Finally, how is UMich generally regarded? I’m also considering Georgetown. Am I right in viewing the latter as more well-regarded for humanities and the former better-known for STEM?
0 replies
missionsqhc
Yesterday at 4:31 PM
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logarithms with natural bases and arguments are rarely studied
CatalinBordea   0
Apr 11, 2025
Are there four natural numbers $ a,b,c,d $ such that $ \log_2 3\cdot\log_5 7=\left(\log_a b\right)^{\log_c d} $ ?
0 replies
CatalinBordea
Apr 11, 2025
0 replies
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logarithms with natural bases and arguments are rarely studied
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CatalinBordea
2142 posts
CatalinBordea
#1 h  Apr 11, 2025, 6:28 AM
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Are there four natural numbers $ a,b,c,d $ such that $ \log_2 3\cdot\log_5 7=\left(\log_a b\right)^{\log_c d} $ ?
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