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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)!

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[*]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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IMO 2014 Problem 4
ipaper   170
N a few seconds ago by lpieleanu
Let $P$ and $Q$ be on segment $BC$ of an acute triangle $ABC$ such that $\angle PAB=\angle BCA$ and $\angle CAQ=\angle ABC$. Let $M$ and $N$ be the points on $AP$ and $AQ$, respectively, such that $P$ is the midpoint of $AM$ and $Q$ is the midpoint of $AN$. Prove that the intersection of $BM$ and $CN$ is on the circumference of triangle $ABC$.

Proposed by Giorgi Arabidze, Georgia.
170 replies
ipaper
Jul 9, 2014
lpieleanu
a few seconds ago
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3^n + 61 is a square
VideoCake   18
N a minute ago by VideoCake
Source: 2025 German MO, Round 4, Grade 11/12, P6
Determine all positive integers \(n\) such that \(3^n + 61\) is the square of an integer.
18 replies
VideoCake
Yesterday at 5:14 PM
VideoCake
a minute ago
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Tilted Students Thoroughly Splash Tiger part 2
DottedCaculator   20
N 11 minutes ago by cj13609517288
Source: ELMO 2024/5
In triangle $ABC$ with $AB<AC$ and $AB+AC=2BC$, let $M$ be the midpoint of $\overline{BC}$. Choose point $P$ on the extension of $\overline{BA}$ past $A$ and point $Q$ on segment $\overline{AC}$ such that $M$ lies on $\overline{PQ}$. Let $X$ be on the opposite side of $\overline{AB}$ from $C$ such that $\overline{AX} \parallel \overline{BC}$ and $AX=AP=AQ$. Let $\overline{BX}$ intersect the circumcircle of $BMQ$ again at $Y \neq B$, and let $\overline{CX}$ intersect the circumcircle of $CMP$ again at $Z \neq C$. Prove that $A$, $Y$, and $Z$ are collinear.

Tiger Zhang
20 replies
DottedCaculator
Jun 21, 2024
cj13609517288
11 minutes ago
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Prefix sums of divisors are perfect squares
CyclicISLscelesTrapezoid   37
N 13 minutes ago by SimplisticFormulas
Source: ISL 2021 N3
Find all positive integers $n$ with the following property: the $k$ positive divisors of $n$ have a permutation $(d_1,d_2,\ldots,d_k)$ such that for $i=1,2,\ldots,k$, the number $d_1+d_2+\cdots+d_i$ is a perfect square.
37 replies
CyclicISLscelesTrapezoid
Jul 12, 2022
SimplisticFormulas
13 minutes ago
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Serbian selection contest for the IMO 2025 - P5
OgnjenTesic   3
N 35 minutes ago by atdaotlohbh
Source: Serbian selection contest for the IMO 2025
Determine the smallest positive real number $\alpha$ such that there exists a sequence of positive real numbers $(a_n)$, $n \in \mathbb{N}$, with the property that for every $n \in \mathbb{N}$ it holds that:
\[ a_1 + \cdots + a_{n+1} < \alpha \cdot a_n. \]Proposed by Pavle Martinović
3 replies
OgnjenTesic
May 22, 2025
atdaotlohbh
35 minutes ago
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Equation in integers with gcd and lcm
skellyrah   1
N 40 minutes ago by frost23
Find all integers \( x \) and \( y \) such that
\[ \frac{1}{\gcd(x, y)} + \frac{3}{xy} + \frac{y}{\operatorname{lcm}(x, y)} = y, \]where \( \gcd(x, y) \) denotes the greatest common divisor of \( x \) and \( y \), and \( \operatorname{lcm}(x, y) \) denotes their least common multiple.
1 reply
skellyrah
an hour ago
frost23
40 minutes ago
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set construction nt
top1vien   1
N an hour ago by alexheinis
Is there a set of 2025 positive integers $S$ that satisfies: for all different $a,b,c,d\in S$, we have $\gcd(ab+1000,cd+1000)=1$?
1 reply
top1vien
Today at 10:04 AM
alexheinis
an hour ago
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A,P,Q lies on the Radical Axis
MrCriminal   3
N an hour ago by Blackbeam999
Source: Power Of a Point -Yufei Zhao #P8
Hint Needed
Let \(ABC\) be a triangle and let \(D\) and \(E\) be points on the sides \(AB\) and \(AC\), respectively , such that \(DE\) is parallel to \(BC\). Let \(P\) be any point interior to triangle \(ADE\) , and let \(F\) and \(G\) be the intersections of \(DE\) with the lines \(BP\) and \(CP\), respectively. Let \(Q\) be the second intersection points of the circumcircles of triangles \(PDG\) and \(PFE\) . Prove that the points \(A, P, \text{and } Q\) are collinear .
3 replies
MrCriminal
May 15, 2021
Blackbeam999
an hour ago
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Hellopoo
Bet667   8
N an hour ago by Aiden-1089
In how many ways can you tile a $3 \cdot n$ rectangle with $2 \cdot 1$ dominoes?
8 replies
Bet667
Yesterday at 11:22 AM
Aiden-1089
an hour ago
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Clifford's chain of circles, concurrent Simson lines
kosmonauten3114   0
an hour ago
Source: My own, but most likely already known
Let $C_1$, $C_2$, $C_3$, $C_4$ be circles having a common point $P$. Denote by $P_{ij}$ the intersection point, other than $P$, of $C_i$ and $C_j$ ($\{i,j\} \in \{1,2,3,4\},i<j$). Let $Q$ be the common point of the 4 circles $\odot(P_{23}P_{24}P_{34})$, $\odot(P_{13}P_{14}P_{34})$, $\odot(P_{12}P_{14}P_{24})$, $\odot(P_{12}P_{13}P_{23})$.
Let $\ell_1$ be the Simson line of $P$ with respect to $\triangle{P_{12}P_{13}P_{14}}$. Define $\ell_2$, $\ell_3$, $\ell_4$ cyclically.
Let $\ell_1'$ be the Simson line of $Q$ with respect to $\triangle{P_{23}P_{24}P_{34}}$. Define $\ell_2'$, $\ell_3'$, $\ell_4'$ cyclically.
Prove that if $\ell_1$, $\ell_2$, $\ell_3$, $\ell_4$ are concurrent, then, $\ell_1'$, $\ell_2'$, $\ell_3'$, $\ell_4'$ are also concurrent.
0 replies
kosmonauten3114
an hour ago
0 replies
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Inequality
srnjbr   4
N an hour ago by sqing
For real numbers a, b, c and d that a+d=b+c prove the following:
(a-b)(c-d)+(a-c)(b-d)+(d-a)(b-c)>=0
4 replies
srnjbr
Oct 30, 2024
sqing
an hour ago
J
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Solution of an interesting inequality
imnotgoodatmathsorry   1
N an hour ago by imnotgoodatmathsorry
Source: @Alphabetamath on Facebook
$\text{The problem:}$
1 reply
imnotgoodatmathsorry
an hour ago
imnotgoodatmathsorry
an hour ago
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Similarity of two triangles!
ariopro1387   1
N an hour ago by Mahdi_Mashayekhi
Source: Iran Team selection test 2025 - P5
In a scalene triangle $ABC$, $D$ is the point of tangency of the incircle with the side $BC$. Points $T_B$ and $T_C$ are the intersections of the angle bisectors of $\angle ABC$ and $\angle ACB$ with the circumcircle of $ABC$, respectively. Let $X_B$ be the antipodal point of $A$ in the circumcircle of $ACD$, and let $X_C$ be the antipodal point of $A$ in the circumcircle of $ABD$.
Prove that triangles $B T_C X_C$ and $C T_B X_B$ are similar.
1 reply
ariopro1387
Today at 10:34 AM
Mahdi_Mashayekhi
an hour ago
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trigonometric inequality
MATH1945   7
N 2 hours ago by sqing
Source: ?
In triangle $ABC$, prove that $$sin^2(A)+sin^2(B)+sin^2(C) \leq \frac{9}{4}$$
7 replies
MATH1945
May 26, 2016
sqing
2 hours ago
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Is it possible that it is not a polynomial
ItzsleepyXD   2
N Apr 26, 2025 by ItzsleepyXD
Source: IDK. Original?
Is it possible that there exist $f: \mathbb{N} \to \mathbb{N}$ such that
$(1)$ $f$ is not a polynomial .
$(2)$ for all $m \neq n \in \mathbb{N}$ , $m-n \mid f(m)-f(n)$ .
2 replies
ItzsleepyXD
Apr 26, 2025
ItzsleepyXD
Apr 26, 2025
J
Is it possible that it is not a polynomial
G H J
Reveal topic tags
algebra
polynomial
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G H BBookmark kLocked kLocked NReply
Source: IDK. Original?
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ItzsleepyXD
150 posts
ItzsleepyXD
#1 h  Apr 26, 2025, 7:26 AM
Y by
Is it possible that there exist $f: \mathbb{N} \to \mathbb{N}$ such that
$(1)$ $f$ is not a polynomial .
$(2)$ for all $m \neq n \in \mathbb{N}$ , $m-n \mid f(m)-f(n)$ .
Z K Y
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E50
8 posts
E50
#2 h  Apr 26, 2025, 7:50 AM
Y by
https://artofproblemsolving.com/community/c6h1379583p7641704
Z K Y
The post below has been deleted. Click to close.
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ItzsleepyXD
150 posts
ItzsleepyXD
#3 h  Apr 26, 2025, 8:38 AM
Y by
thanks :D
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