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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
Inequalities
sqing   7
N 40 minutes ago by ytChen
Let $ a,b>0   $ . Prove that
$$ \frac{a}{a^2+a +2b+1}+ \frac{b}{b^2+2a +b+1}  \leq  \frac{2}{5} $$$$ \frac{a}{a^2+2a +b+1}+ \frac{b}{b^2+a +2b+1}  \leq  \frac{2}{5} $$
7 replies
sqing
May 13, 2025
ytChen
40 minutes ago
Functional equation
Pmshw   18
N an hour ago by jasperE3
Source: Iran 2nd round 2022 P2
Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for any real value of $x,y$ we have:
$$f(xf(y)+f(x)+y)=xy+f(x)+f(y)$$
18 replies
Pmshw
May 8, 2022
jasperE3
an hour ago
f(x)f(yf(x)) = f(x+y)
ISHO95   5
N an hour ago by jasperE3
Find all functions $f:\mathbb R^+ \to \mathbb R^+$, for all $x,y \in \mathbb R^+$, \[ f(x)f(yf(x))=f(x+y). \]
5 replies
ISHO95
Jan 14, 2013
jasperE3
an hour ago
Two players want to obtain a number divisible by 2023
a_507_bc   3
N an hour ago by fathalishah
Source: All-Russian MO 2023 Final stage 11.5
Initially, $10$ ones are written on a blackboard. Grisha and Gleb are playing game, by taking turns; Grisha goes first. On one move Grisha squares some $5$ numbers on the board. On his move, Gleb picks a few (perhaps none) numbers on the board and increases each of them by $1$. If in $10,000$ moves on the board a number divisible by $2023$ appears, Gleb wins, otherwise Grisha wins. Which of the players has a winning strategy?
3 replies
a_507_bc
Apr 23, 2023
fathalishah
an hour ago
Points on a lattice path lies on a line
navi_09220114   1
N an hour ago by pbornsztein
Source: TASIMO 2025 Day 1 Problem 3
Let $S$ be a nonempty subset of the points in the Cartesian plane such that for each $x\in S$ exactly one of $x+(0,1)$ or $x+(1,0)$ also belongs to $S$. Prove that for each positive integer $k$ there is a line in the plane (possibly different lines for different $k$) which contains at least $k$ points of $S$.
1 reply
navi_09220114
Today at 11:43 AM
pbornsztein
an hour ago
Functional inequality
Jackson0423   2
N 2 hours ago by nitride
Show that there does not exist a function \( f : \mathbb{R}^+ \to \mathbb{R}^+ \) such that for all positive real numbers \( x, y \),
\[
f^2(x) \geq f(x+y)\left(f(x) + y\right).
\]
2 replies
Jackson0423
5 hours ago
nitride
2 hours ago
Vieta's Relation
P162008   1
N 2 hours ago by vanstraelen
If $\alpha, \beta$ and $\gamma$ are the roots of the cubic equation $x^3 - x^2 - 2x + 1 = 0$ then compute $\sum_{cyc} (\alpha + \beta)^{1/3}.$
1 reply
P162008
Today at 10:38 AM
vanstraelen
2 hours ago
no of integer soultions of ||x| - 2020| < 5 - IOQM 2020-21 p5
parmenides51   12
N 2 hours ago by Yiyj
Find the number of integer solutions to $||x| - 2020| < 5$.
12 replies
parmenides51
Jan 18, 2021
Yiyj
2 hours ago
Find all integers
velmurugan   3
N 2 hours ago by grupyorum
Source: Titu and Dorin Book Problem
Find all positive integers $(x,n)$ such that $x^n + 2^n + 1$ is a divisor of $x^{n+1} + 2^{n+1} +1 $ .
3 replies
velmurugan
Jul 30, 2015
grupyorum
2 hours ago
Graph Process Problem
Maximilian113   10
N 2 hours ago by Ru83n05
Source: CMO 2025 P1
The $n$ players of a hockey team gather to select their team captain. Initially, they stand in a circle, and each person votes for the person on their left.

The players will update their votes via a series of rounds. In one round, each player $a$ updates their vote, one at a time, according to the following procedure: At the time of the update, if $a$ is voting for $b,$ and $b$ is voting for $c,$ then $a$ updates their vote to $c.$ (Note that $a, b,$ and $c$ need not be distinct; if $b=c$ then $a$'s vote does not change for this update.) Every player updates their vote exactly once in each round, in an order determined by the players (possibly different across different rounds).

They repeat this updating procedure for $n$ rounds. Prove that at this time, all $n$ players will unanimously vote for the same person.
10 replies
Maximilian113
Mar 7, 2025
Ru83n05
2 hours ago
Congrats to former two perfect scorer in IMO
mszew   0
2 hours ago
Source: Where should it be posted?
Congrats to the new president of Romania...Mr. Nicuşor Dan

https://en.wikipedia.org/wiki/Nicu%C8%99or_Dan

https://www.imo-official.org/participant_r.aspx?id=1571
0 replies
mszew
2 hours ago
0 replies
Austrian Regional MO 2025 P4
BR1F1SZ   3
N 2 hours ago by LeYohan
Source: Austrian Regional MO
Let $z$ be a positive integer that is not divisible by $8$. Furthermore, let $n \geqslant 2$ be a positive integer. Prove that none of the numbers of the form $z^n + z + 1$ is a square number.

(Walther Janous)
3 replies
BR1F1SZ
Apr 18, 2025
LeYohan
2 hours ago
Docked 4 points Help
sadas123   9
N 2 hours ago by ethan2011
In school we had this beginners like middle school contest, but we had to right down our solution kind of like usajmo except no proofs. It was also graded out of 7 but I got 4 Points docked for this question. what was my problem??? But I kind of had to rush the solution on this question because there was another problem before this that was like 1000x times harder.

Question:The solutions to the equation x^3-13x^2+ax−48=0 are all positive whole numbers. What is $a$?


Solution: We can see that we can use Vieta's formulas to find that the product of the roots is $48$, and the sum of the roots is $13$. So we need to find a combination of integers that multiply to $48$ and add up to $13$. Let's call the roots of the equation p, q, and r. From Vieta's, we get that $p+q+r=-13$ and $pqr = -48$. Looking at the factors of $48$, which is $2^4*3$, we try to split the numbers in a way that gives us the correct sum and product. Trying 3, -2, and -8, we see that they add up to $-13$ and multiply to $-48$, so they work. That means the roots of the polynomial are -3, -2, and -8, and the factorization is $(x-3)(x-2)(x-8)$. Multiplying it out, we get $x^3-13x^2+46x-48$, so we find that a = 46.
9 replies
sadas123
Yesterday at 4:06 PM
ethan2011
2 hours ago
Nice concurrency
navi_09220114   3
N 3 hours ago by sami1618
Source: TASIMO 2025 Day 1 Problem 2
Four points $A$, $B$, $C$, $D$ lie on a semicircle $\omega$ in this order with diameter $AD$, and $AD$ is not parallel to $BC$. Points $X$ and $Y$ lie on segments $AC$ and $BD$ respectively such that $BX\parallel AD$ and $CY\perp AD$. A circle $\Gamma$ passes through $D$ and $Y$ is tangent to $AD$, and intersects $\omega$ again at $Z\neq D$. Prove that the lines $AZ$, $BC$ and $XY$ are concurrent.
3 replies
navi_09220114
Today at 11:42 AM
sami1618
3 hours ago
Sequence problem I never used
Sedro   1
N Apr 24, 2025 by mathprodigy2011
Let $\{a_n\}_{n\ge 1}$ be a sequence of reals such that $a_1=1$ and $a_{n+1}a_n = 3a_n+2$ for all positive integers $n$. As $n$ grows large, the value of $a_{n+2}a_{n+1}a_n$ approaches the real number $M$. What is the greatest integer less than $M$?
1 reply
Sedro
Apr 24, 2025
mathprodigy2011
Apr 24, 2025
Sequence problem I never used
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Sedro
5850 posts
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Let $\{a_n\}_{n\ge 1}$ be a sequence of reals such that $a_1=1$ and $a_{n+1}a_n = 3a_n+2$ for all positive integers $n$. As $n$ grows large, the value of $a_{n+2}a_{n+1}a_n$ approaches the real number $M$. What is the greatest integer less than $M$?
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mathprodigy2011
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#2 • 1 Y
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