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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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0 replies
jlacosta
Apr 2, 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
J
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Invariant board combi style
ItzsleepyXD   1
N 15 minutes ago by waterbottle432
Source: Own , Mock Thailand Mathematic Olympiad P7
Oh write $2025^{2025^{2025}}$ real number on the board such that each number is more than $2025^{2025}$ .
Oh erase 2 number $x,y$ on the board and write $\frac{xy-2025}{x+y-90}$ .
Prove that the last number will always be the same regardless the order of number that Oh pick .
1 reply
ItzsleepyXD
an hour ago
waterbottle432
15 minutes ago
J
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weird Condition
B1t   8
N 16 minutes ago by lolsamo
Source: Mongolian TST 2025 P4
deleted for a while
8 replies
B1t
Apr 27, 2025
lolsamo
16 minutes ago
J
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D1025 : Can you do that?
Dattier   3
N 17 minutes ago by Dattier
Source: les dattes à Dattier
Let $x_{n+1}=x_n^3$ and $x_0=3$.

Can you calculate $\sum\limits_{i=1}^{2^{2025}} x_i \mod 10^{30}$?
3 replies
Dattier
Yesterday at 8:24 PM
Dattier
17 minutes ago
J
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Parallel condition and isogonal
ItzsleepyXD   1
N 25 minutes ago by moony_
Source: Own , Mock Thailand Mathematic Olympiad P5
Let $ABC$ be triangle and point $D$ be $A-$ altitude of $\triangle ABC$ .
Let $E,F$ be a point on $AC$ and $AB$ such that $DE\parallel AB$ and $DF\parallel AC$ . Point $G$ is the intersection of $(AEF)$ and $(ABC)$ . Point $P$ be intersection of $(ADG)$ and $BC$ . Line $GD$ intersect circumcircle of $\triangle ABC$ again at $Q$ .
Prove that
(a) $\angle BAP = \angle QAC$ .
(b) $AQ$ bisect $BC$ .
1 reply
ItzsleepyXD
2 hours ago
moony_
25 minutes ago
J
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RMM 2013 Problem 1
dr_Civot   31
N 36 minutes ago by cursed_tangent1434
For a positive integer $a$, define a sequence of integers $x_1,x_2,\ldots$ by letting $x_1=a$ and $x_{n+1}=2x_n+1$ for $n\geq 1$. Let $y_n=2^{x_n}-1$. Determine the largest possible $k$ such that, for some positive integer $a$, the numbers $y_1,\ldots,y_k$ are all prime.
31 replies
dr_Civot
Mar 2, 2013
cursed_tangent1434
36 minutes ago
J
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Inspired by old results
sqing   0
36 minutes ago
Source: Own
Let $ a , b , c>0 $and $ abc=1 $. Prove that
$$\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a} +3 \geq \frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$$h
0 replies
sqing
36 minutes ago
0 replies
J
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amazing balkan combi
egxa   7
N 38 minutes ago by Assassino9931
Source: BMO 2025 P4
There are $n$ cities in a country, where $n \geq 100$ is an integer. Some pairs of cities are connected by direct (two-way) flights. For two cities $A$ and $B$ we define:

$(i)$ A $\emph{path}$ between $A$ and $B$ as a sequence of distinct cities $A = C_0, C_1, \dots, C_k, C_{k+1} = B$, $k \geq 0$, such that there are direct flights between $C_i$ and $C_{i+1}$ for every $0 \leq i \leq k$;
$(ii)$ A $\emph{long path}$ between $A$ and $B$ as a path between $A$ and $B$ such that no other path between $A$ and $B$ has more cities;
$(iii)$ A $\emph{short path}$ between $A$ and $B$ as a path between $A$ and $B$ such that no other path between $A$ and $B$ has fewer cities.
Assume that for any pair of cities $A$ and $B$ in the country, there exist a long path and a short path between them that have no cities in common (except $A$ and $B$). Let $F$ be the total number of pairs of cities in the country that are connected by direct flights. In terms of $n$, find all possible values $F$

Proposed by David-Andrei Anghel, Romania.
7 replies
egxa
Apr 27, 2025
Assassino9931
38 minutes ago
J
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Question on Balkan SL
Fmimch   2
N 40 minutes ago by Assassino9931
Does anyone know where to find the Balkan MO Shortlist 2024? If you have the file, could you send in this thread? Thank you!
2 replies
Fmimch
Today at 12:13 AM
Assassino9931
40 minutes ago
J
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Or statement function
ItzsleepyXD   1
N 43 minutes ago by Haris1
Source: Own , Mock Thailand Mathematic Olympiad P2
Find all $f: \mathbb{R} \to \mathbb{Z^+}$ such that $$f(x+f(y))=f(x)+f(y)+1\quad\text{ or }\quad f(x)+f(y)-1$$for all real number $x$ and $y$
1 reply
ItzsleepyXD
2 hours ago
Haris1
43 minutes ago
J
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Add a digit to obtain a new perfect square
Lukaluce   2
N an hour ago by TopGbulliedU
Source: 2024 Junior Macedonian Mathematical Olympiad P4
Let $a_1, a_2, ..., a_n$ be a sequence of perfect squares such that $a_{i + 1}$ can be obtained by concatenating a digit to the right of $a_i$. Determine all such sequences that are of maximum length.

Proposed by Ilija Jovčeski
2 replies
Lukaluce
Apr 14, 2025
TopGbulliedU
an hour ago
J
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Simple inequality
sqing   7
N an hour ago by sqing
Source: Daniel Sitaru
Let $a,b,c>0$ . Prove that$$\frac{a^3}{b^3}+\frac{b^3}{c^3}+\frac{c^3}{a^3}+9>\frac{3}{2}\left(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}+ \frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)$$
7 replies
sqing
Feb 10, 2017
sqing
an hour ago
J
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Vector Vortex
steven_zhang123   1
N an hour ago by Mathzeus1024
Source: NS Issue 1 P3 (2014.4)
Let $v_{1}, v_{2}, \cdots, v_{n}$ be $n$ unit vectors on a plane, where $n$ is an odd number. Prove that there exist $\varepsilon _i\in \left \{ -1,1 \right \} $ for $i=1,2,\cdots,n$ such that $\left | \sum_{i=1}^{n} \varepsilon_i v_i \right | \le 1.$
1 reply
steven_zhang123
Feb 15, 2025
Mathzeus1024
an hour ago
J
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China Northern MO 2009 p4 CNMO
parkjungmin   0
an hour ago
Source: China Northern MO 2009 p4 CNMO P4
The problem is too difficult.
0 replies
parkjungmin
an hour ago
0 replies
J
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The Appetizer of Iran NT2023
alinazarboland   6
N an hour ago by A22-
Source: Iran MO 3rd round 2023 NT exam , P1
Find all integers $n > 4$ st for every two subsets $A,B$ of $\{0,1,....,n-1\}$ , there exists a polynomial $f$ with integer coefficients st either $f(A) = B$ or $f(B) = A$ where the equations are considered mod n.
We say two subsets are equal mod n if they produce the same set of reminders mod n. and the set $f(X)$ is the set of reminders of $f(x)$ where $x \in X$ mod n.
6 replies
alinazarboland
Aug 17, 2023
A22-
an hour ago
J
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J
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EGMO Genre Predictions
ohiorizzler1434   23
N Apr 15, 2025 by ItsBesi
Everybody, with EGMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
23 replies
ohiorizzler1434
Mar 28, 2025
ItsBesi
Apr 15, 2025
J
EGMO Genre Predictions
G H J
Reveal topic tags
EGMO
L
G H BBookmark kLocked kLocked NReply
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ohiorizzler1434
761 posts
ohiorizzler1434
#1 h  Mar 28, 2025, 4:16 AM • 3 Y
Y by OronSH, Exponent11, ihatemath123
Everybody, with EGMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
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sixoneeight
1138 posts
sixoneeight
#2 h  Mar 28, 2025, 4:36 AM
Y by
CAG AGC (no N of course)
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Haris1
76 posts
Haris1
#3 h  Mar 28, 2025, 8:54 AM • 2 Y
Y by Sadigly, farhad.fritl
AAA GGG trust triple fe incoming with length geos in day 2. :ninja:
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BR1F1SZ
562 posts
BR1F1SZ
#4 h  Mar 28, 2025, 10:07 AM
Y by
Do the IMO rules apply? (i.e. must problems $1$, $2$, $4$, $5$ be different subjects?)
This post has been edited 1 time. Last edited by BR1F1SZ, Mar 28, 2025, 10:07 AM
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alexanderhamilton124
389 posts
alexanderhamilton124
#5 h  Mar 28, 2025, 10:58 AM • 1 Y
Y by L13832
im not sure @above

im hoping for ANGNCA
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BR1F1SZ
562 posts
BR1F1SZ
#6 h  Mar 28, 2025, 11:00 AM
Y by
BR1F1SZ wrote:
Do the IMO rules apply? (i.e. must problems $1$, $2$, $4$, $5$ be different subjects?)

I guess NCG GAC
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NicoN9
130 posts
NicoN9
#7 h  Mar 28, 2025, 11:15 AM
Y by
I guess GAN CNG
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maths_enthusiast_0001
133 posts
maths_enthusiast_0001
#8 h  Mar 28, 2025, 11:21 AM
Y by
GGG GGG
:ddr: :gathering:
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GreekIdiot
208 posts
GreekIdiot
#9 h  Mar 28, 2025, 2:40 PM
Y by
CCC CCC
:whistling:
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ItsBesi
144 posts
ItsBesi
#10 h  Mar 28, 2025, 3:21 PM • 3 Y
Y by NicoN9, farhad.fritl, Funcshun840
Happy that EGMO will be organised on my country (KOSOVO) I hope it's going to be:GCA NAG :play_ball:
This post has been edited 1 time. Last edited by ItsBesi, Mar 28, 2025, 7:15 PM
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bjump
1007 posts
bjump
#11 h  Mar 28, 2025, 3:37 PM
Y by
CNA ACN

Geometry is dead :(
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Jupiterballs
42 posts
Jupiterballs
#12 h  Mar 28, 2025, 3:41 PM
Y by
Hmm, maybe AGC ANG
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Primeniyazidayi
84 posts
Primeniyazidayi
#13 h  Mar 28, 2025, 3:51 PM • 1 Y
Y by Gato_combinatorio
I hope GCA GNA. At least I can solve geos and pretend that I'm good at geo:)
This post has been edited 1 time. Last edited by Primeniyazidayi, Mar 28, 2025, 3:52 PM
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amburger
5 posts
amburger
#14 h  Mar 28, 2025, 9:41 PM
Y by
imagine if they pull up with a p3 level A like last yr;s p6
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amburger
5 posts
amburger
#15 h  Mar 28, 2025, 9:41 PM
Y by
oh god i hope as little A as possible egmo A tends to be so bashy

2024 p5 was so bad
This post has been edited 1 time. Last edited by amburger, Mar 28, 2025, 9:44 PM
Reason: f
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ItsBesi
144 posts
ItsBesi
#16 h  Apr 14, 2025, 8:38 AM • 1 Y
Y by NicoN9
ItsBesi wrote:
Happy that EGMO will be organised on my country (KOSOVO) I hope it's going to be:GCA NAG :play_ball:

Just as I predicted (day 2-day 1)
This post has been edited 1 time. Last edited by ItsBesi, Apr 14, 2025, 8:38 AM
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NicoN9
130 posts
NicoN9
#17 h  Apr 14, 2025, 12:16 PM
Y by
ItsBesi wrote:
ItsBesi wrote:
Happy that EGMO will be organised on my country (KOSOVO) I hope it's going to be:GCA NAG :play_ball:

Just as I predicted (day 2-day 1)

Wait how did you predict that? P5 with turbo is nice
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Ywgh1
139 posts
Ywgh1
#18 h  Apr 14, 2025, 12:49 PM
Y by
ohiorizzler1434 wrote:
Everybody, with EGMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict

Great guess honestly
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damathgoat
232 posts
damathgoat
#19 h  Apr 14, 2025, 12:52 PM
Y by
yeah what he said
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ohiorizzler1434
761 posts
ohiorizzler1434
#20 h  Apr 14, 2025, 1:22 PM
Y by
Amazing! The EGMO problems have all been released! The genres are:

NAG
GCC

What a surprising outcome!
This post has been edited 1 time. Last edited by ohiorizzler1434, Apr 14, 2025, 1:22 PM
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khina
993 posts
khina
#21 h  Apr 14, 2025, 5:56 PM • 1 Y
Y by NicoN9
In what way is problem 6 C (other than requiring an $n \times n$ board)? To me the problem seems to be entirely algebra; there is no combinatorics element since you aren't counting anything.
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NicoN9
130 posts
NicoN9
#22 h  Apr 14, 2025, 9:57 PM
Y by
Yeah it was NAG GCA I think
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jkim0656
1013 posts
jkim0656
#23 h  Apr 14, 2025, 10:02 PM
Y by
was the last one C or A?
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ItsBesi
144 posts
ItsBesi
#24 h  Apr 15, 2025, 4:21 PM • 1 Y
Y by NicoN9
NicoN9 wrote:
ItsBesi wrote:
ItsBesi wrote:
Happy that EGMO will be organised on my country (KOSOVO) I hope it's going to be:GCA NAG :play_ball:

Just as I predicted (day 2-day 1)

Wait how did you predict that? P5 with turbo is nice

I also predicted about Turbo, people thinking I cheated because it was held in my country but I didn’t do that I just had a feeling about it.
This post has been edited 2 times. Last edited by ItsBesi, Apr 15, 2025, 4:23 PM
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