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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
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
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Inequality involving semiperimeter
Sadigly   2
N a minute ago by ehuseyinyigit
Source: Azerbaijan Junior NMO 2019
Prove that, for any triangle with side lengths $a,b,c$, the following inequality holds $$\frac{a}{(b+c)^2}+\frac{b}{(c+a)^2}+\frac{c}{(a+b)^2}\geq\frac9{8p}$$($p$ denotes the semiperimeter of a triangle)
2 replies
Sadigly
18 minutes ago
ehuseyinyigit
a minute ago
J
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Somewhat ugly equation
Sadigly   0
2 minutes ago
Source: Azerbaijan Senior NMO 2019
Solve the following equation $$\sqrt{\frac{x^2}3-ax+a^2}+\sqrt{\frac{x^2}3-bx+b^2}=\sqrt{a^2-ab+b^2}$$where $a;b\in\mathbb{R^+}$
0 replies
Sadigly
2 minutes ago
0 replies
J
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Cyclic Quads and Parallel Lines
gracemoon124   18
N 10 minutes ago by busy-beaver
Source: 2015 British Mathematical Olympiad?
Let $ABCD$ be a cyclic quadrilateral. Let $F$ be the midpoint of the arc $AB$ of its circumcircle which does not contain $C$ or $D$. Let the lines $DF$ and $AC$ meet at $P$ and the lines $CF$ and $BD$ meet at $Q$. Prove that the lines $PQ$ and $AB$ are parallel.
18 replies
gracemoon124
Aug 16, 2023
busy-beaver
10 minutes ago
J
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Find all integers satisfying this equation
Sadigly   0
13 minutes ago
Source: Azerbaijan NMO 2019
Find all $x;y\in\mathbb{Z}$ satisfying the following condition: $$x^3=y^4+9x^2$$
0 replies
Sadigly
13 minutes ago
0 replies
J
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Shortest number theory you might've seen in your life
AlperenINAN   2
N 13 minutes ago by zuat.e
Source: Turkey JBMO TST 2025 P4
Let $p$ and $q$ be prime numbers. Prove that if $pq(p+1)(q+1)$ is a perfect square, then $pq + 1$ is also a perfect square.
2 replies
AlperenINAN
an hour ago
zuat.e
13 minutes ago
J
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Is this even algebra or geometry
Sadigly   3
N 14 minutes ago by Moon_settler
Source: Azerbaijan Junior NMO 2019
Alice creates the graphs $y=|x-a|$ and $y=c-|x-b|$ , where $a,b,c\in\mathbb{R^+}$. She observes that these two graphs and $x$ axis divides the positive side of the plane ($x,y>0$) into two triangles and a quadrilateral. Find the ratio of sums of two triangles' areas to the area of quadrilateral.
3 replies
Sadigly
23 minutes ago
Moon_settler
14 minutes ago
J
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Prove or disprove the existence of such a
Sadigly   0
21 minutes ago
Source: Azerbaijan NMO
A positive number $a$ is given, such that $a$ could be expressed as difference of two perfect squares ($a=\frac1{n^2}-\frac1{m^2}$). Is it possible for $2a$ to be expressed as difference of two perfect squares?
0 replies
Sadigly
21 minutes ago
0 replies
J
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Points on the sides of cyclic quadrilateral satisfy the angle conditions
AlperenINAN   1
N 26 minutes ago by ehuseyinyigit
Source: Turkey JBMO TST 2025 P1
Let $ABCD$ be a cyclic quadrilateral and let the intersection point of lines $AB$ and $CD$ be $E$. Let the points $K$ and $L$ be arbitrary points on sides $CD$ and $AB$ respectively, which satisfy the conditions
$$\angle KAD = \angle KBC \quad \text{and} \quad \angle LDA = \angle LCB.$$Prove that $EK = EL$.
1 reply
AlperenINAN
an hour ago
ehuseyinyigit
26 minutes ago
J
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Writing quadratic trinomials inside cells
Sadigly   0
29 minutes ago
Source: Azerbaijan Junior NMO 2019
A $6\times6$ square is given, and a quadratic trinomial with a positive leading coefficient is placed in each of its cells. There are $108$ coefficents in total, and these coefficents are chosen from the set $[-66;47]$, and each coefficient is different from each other. Prove that there exists at least one column such that the sum of the six trinomials in that column has a real root.
0 replies
Sadigly
29 minutes ago
0 replies
J
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Product of consecutive terms divisible by a prime number
BR1F1SZ   1
N 30 minutes ago by IndoMathXdZ
Source: 2025 Francophone MO Seniors P4
Determine all sequences of strictly positive integers $a_1, a_2, a_3, \ldots$ satisfying the following two conditions:
[list]
[*]There exists an integer $M > 0$ such that, for all indices $n \geqslant 1$, $0 < a_n \leqslant M$.
[*]For any prime number $p$ and for any index $n \geqslant 1$, the number
\[ a_n a_{n+1} \cdots a_{n+p-1} - a_{n+p} \]is a multiple of $p$.
[/list]


1 reply
1 viewing
BR1F1SZ
Today at 12:09 AM
IndoMathXdZ
30 minutes ago
J
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Minimum value of a 3 variable expression
bin_sherlo   3
N 34 minutes ago by ehuseyinyigit
Source: Türkiye 2025 JBMO TST P6
Find the minimum value of
\[\frac{x^3+1}{(y-1)(z+1)}+\frac{y^3+1}{(z-1)(x+1)}+\frac{z^3+1}{(x-1)(y+1)}\]where $x,y,z>1$ are reals.
3 replies
bin_sherlo
an hour ago
ehuseyinyigit
34 minutes ago
J
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Incenter is the foot of altitude
Sadigly   0
an hour ago
Source: Azerbaijan JBMO TST 2023
Let $ABC$ be a triangle and let $\Omega$ denote the circumcircle of $ABC$. The foot of altitude from $A$ to $BC$ is $D$. The foot of altitudes from $D$ to $AB$ and $AC$ are $K;L$ , respectively. Let $KL$ intersect $\Omega$ at $X;Y$, and let $AD$ intersect $\Omega$ at $Z$. Prove that $D$ is the incenter of triangle $XYZ$
0 replies
Sadigly
an hour ago
0 replies
J
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System of equations in juniors' exam
AlperenINAN   1
N an hour ago by AlperenINAN
Source: Turkey JBMO TST 2025 P3
Find all positive real solutions $(a, b, c)$ to the following system:
$$ \begin{aligned} a^2 + \frac{b}{a} &= 8, \\ ab + c^2 &= 18, \\ 3a + b + c &= 9\sqrt{3}. \end{aligned} $$
1 reply
AlperenINAN
an hour ago
AlperenINAN
an hour ago
J
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reals associated with 1024 points
bin_sherlo   0
an hour ago
Source: Türkiye 2025 JBMO TST P8
Pairwise distinct points $P_1,\dots,P_{1024}$, which lie on a circle, are marked by distinct reals $a_1,\dots,a_{1024}$. Let $P_i$ be $Q-$good for a $Q$ on the circle different than $P_1,\dots,P_{1024}$, if and only if $a_i$ is the greatest number on at least one of the two arcs $P_iQ$. Let the score of $Q$ be the number of $Q-$good points on the circle. Determine the greatest $k$ such that regardless of the values of $a_1,\dots,a_{1024}$, there exists a point $Q$ with score at least $k$.
0 replies
bin_sherlo
an hour ago
0 replies
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/ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
mqoi_KOLA   1
N Apr 12, 2025 by EeEApO
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1 reply
mqoi_KOLA
Apr 12, 2025
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