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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Yesterday at 3:18 PM
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.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
1 viewing
jlacosta
Yesterday at 3:18 PM
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
2⁠0⁠⁠2⁠4
Technodoggo   71
N 2 minutes ago by RedChameleon
Happy New Year!
To celebrate the start of 2024, I've decided to put up a few facts about the year. I don't have many, so y'all should also

1

2

(1 and 2 are the same :sob: just distribute)

Post more cool facts here! Keep a running chain with quote boxes for facts. (I don't know if this technically qualifies as a marathon, but I hope this is allowed lol)
71 replies
Technodoggo
Jan 1, 2024
RedChameleon
2 minutes ago
2025 MATHCOUNTS State Hub
SirAppel   218
N 2 minutes ago by MC_ADe
Previous Years' "Hubs": (2022) (2023) (2024)Please Read

Now that it's April and we're allowed to discuss, and no one else has made this yet ...
[list=disc]
[*] CA: 43 (45 44 43 43 43 42 42 41 41 41)
[*] NJ: 43 (45 44 44 43 39 42 40 40 39 38) *
[*] NY: 42 (43 42 42 42 41 40)
[*] TX: 42 (43 43 43 42 42 40 40 38 38 38)
[*] MA: 41 (45 43 42 41)
[*] WA: 41 (41 45 42 41 41 41 41 41 41 40) *
[*] FL: 39 (42 41 40 39 38 37 37)
[*] IN: 39 (41 40 40 39 36 35 35 35 34 34)
[*] NC: 39 (42 42 41 39)
[*] IL: 38 (41 40 39 38 38 38)
[*] OR: 38 (44 41? 38 38)
[*] PA: 38 (41 40 40 38 38 37 36 36 34 34) *
[*] MD: 37 (43 39 39 37 37 37)
[*] CT: 36 (44 39? 38 36 34 34 34 34)
[*] MI: 36 (39 41 41 36 37 37 36 36 36 36) *
[*] MN: 36 (40 36 36 36 35 35 35 34)
[*] CO: 35 (41 37 37 35 35 35 ?? 31 31 30) *
[*] GA: 35 (38 37 36 35 34 34 34 34 34 33)
[*] OH: 35 (41 37 36 35)
[*] AR: 34 (46 45 35 34 33 31 31 31 29 29)
[*] WI: 34 (40 37 37 34 35 30 28 29 29 29) *
[*] NH: 31 (42 35 33 31 30)
[*] DE: 30 (34 33 32 30 30 29 28 27 26? 24)
[*] SC: 30 (33 33 31 30)
[*] IA: 29 (33 30 31 29 29 29 29 29 29 29 29 29) *
[*] NE: 28 (34 30 28 28 27 27 26 26 25 25)
[*] SD: 22 (30 29 24 22 22 22 21 21 20 20)
[/list]
Cutoffs Unknown

* means that CDR is official in that state.

Notes

For those asking about the removal of the tiers, I'd like to quote Jason himself:
[quote=peace09]
learn from my mistakes
[/quote]

Help contribute by sharing your state's cutoffs!
As per last year's guidelines, refrain from problem discussion until their official release on the MATHCOUNTS website.
218 replies
+2 w
SirAppel
Apr 1, 2025
MC_ADe
2 minutes ago
Simple problem on percentages
ohiorizzler1434   9
N 3 minutes ago by RedChameleon
Fanum and Kai Cenat are getting taxed. If Fanum's tax increases by 60%, then Fanum will be taxed 24 dollars. If Kai Cenat's tax increases by 20%, then he would also be taxed 24 dollars.

How much more is Kai Cenat taxed than Fanum?
9 replies
ohiorizzler1434
Feb 20, 2024
RedChameleon
3 minutes ago
FTW tournament!
evt917   9
N 22 minutes ago by Yrock
[center]Since all FTW tournaments have dramatically failed, I'm trying a different format. Here is how it works:

1. Type \signup{your rating (type 800 for unrated)}

2. You will eventually be assigned to a game. I will be doing this. how i assign games

3. If you win, you get 2 points. However, if you win games in a row, you get more points per win. When you win $n$ games in a row, you score $n+1$ points instead of $2$ points. Nice, right? A tie equals $1$ point, and a loss is zero. A tie or a loss will break your win streak.

4. I do not know everybody's time preferences. Because so, I will announce in advance which two players will be playing, so they themselves can organize a game themselves. Remember, THE PLAYERS ARE ORGANIZING THE GAMES THEMSELVES!!! The format is up to them, but please make the time control at least 20 seconds. Please announce the results of the game here so i can update the scoreboard. Games can be unrated.

recommended format if you cannot decide



5. The tournament goes on until april 22nd! Extremely long, right? Note that you can still signup after the first games has started, but you will have a disadvantage because some people who signed up as soon as the tournament started already has points.

6. Once you are done with your game, I will pair you with another opponent. You may play against same people multiple times. You can also request a new partner if your's is inactive and doesn't want to play.


[rule]

Questions and Answers

All signups and ratings

[rule]

LIVE LEADERBOARD:

1st place:
2nd place:
3rd place

4th place:
5th place:
9 replies
evt917
an hour ago
Yrock
22 minutes ago
Unsolved NT, 3rd time posting
GreekIdiot   8
N 2 hours ago by ektorasmiliotis
Source: own
Solve $5^x-2^y=z^3$ where $x,y,z \in \mathbb Z$
Hint
8 replies
GreekIdiot
Mar 26, 2025
ektorasmiliotis
2 hours ago
n=y^2+108
Havu   6
N 2 hours ago by ektorasmiliotis
Given the positive integer $n = y^2 + 108$ where $y \in \mathbb{N}$.
Prove that $n$ cannot be a perfect cube of a positive integer.
6 replies
Havu
Today at 4:30 PM
ektorasmiliotis
2 hours ago
Valuable subsets of segments in [1;n]
NO_SQUARES   0
2 hours ago
Source: Russian May TST to IMO 2023; group of candidates P6; group of non-candidates P8
The integer $n \geqslant 2$ is given. Let $A$ be set of all $n(n-1)/2$ segments of real line of type $[i, j]$, where $i$ and $j$ are integers, $1\leqslant i<j\leqslant n$. A subset $B \subset A$ is said to be valuable if the intersection of any two segments from $B$ is either empty, or is a segment of nonzero length belonging to $B$. Find the number of valuable subsets of set $A$.
0 replies
NO_SQUARES
2 hours ago
0 replies
Fneqn or Realpoly?
Mathandski   2
N 3 hours ago by jasperE3
Source: India, not sure which year. Found in OTIS pset
Find all polynomials $P$ with real coefficients obeying
\[P(x) P(x+1) = P(x^2 + x + 1)\]for all real numbers $x$.
2 replies
Mathandski
5 hours ago
jasperE3
3 hours ago
thanks u!
Ruji2018252   2
N 3 hours ago by CHESSR1DER
find all $f: \mathbb{R}\to \mathbb{R}$ and
\[(x-y)[f(x)+f(y)]\leqslant f(x^2-y^2), \forall x,y \in \mathbb{R}\]
2 replies
1 viewing
Ruji2018252
5 hours ago
CHESSR1DER
3 hours ago
Functional equations
hanzo.ei   11
N 5 hours ago by GreekIdiot
Source: Greekldiot
Find all $f: \mathbb R_+ \rightarrow \mathbb R_+$ such that $f(xf(y)+f(x))=yf(x+yf(x)) \: \forall \: x,y \in \mathbb R_+$
11 replies
hanzo.ei
Mar 29, 2025
GreekIdiot
5 hours ago
D1018 : Can you do that ?
Dattier   1
N 5 hours ago by Dattier
Source: les dattes à Dattier
We can find $A,B,C$, such that $\gcd(A,B)=\gcd(C,A)=\gcd(A,2)=1$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$.

For example :

$C=20$
$A=47650065401584409637777147310342834508082136874940478469495402430677786194142956609253842997905945723173497630499054266092849839$

$B=238877301561986449355077953728734922992395532218802882582141073061059783672634737309722816649187007910722185635031285098751698$

Can you find $A,B,C$ such that $A>3$ is prime, $C,B \in (\mathbb Z/A\mathbb Z)^*$ with $o(C)=(A-1)/2$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$?
1 reply
Dattier
Mar 24, 2025
Dattier
5 hours ago
D1010 : How it is possible ?
Dattier   14
N 5 hours ago by ehuseyinyigit
Source: les dattes à Dattier
Is it true that$$\forall n \in \mathbb N^*, (24^n \times B \mod A) \mod 2 = 0 $$?

A=1728400904217815186787639216753921417860004366580219212750904
024377969478249664644267971025952530803647043121025959018172048
336953969062151534282052863307398281681465366665810775710867856
720572225880311472925624694183944650261079955759251769111321319
421445397848518597584590900951222557860592579005088853698315463
815905425095325508106272375728975

B=2275643401548081847207782760491442295266487354750527085289354
965376765188468052271190172787064418854789322484305145310707614
546573398182642923893780527037224143380886260467760991228567577
953725945090125797351518670892779468968705801340068681556238850
340398780828104506916965606659768601942798676554332768254089685
307970609932846902
14 replies
Dattier
Mar 10, 2025
ehuseyinyigit
5 hours ago
iran tst 2018 geometry
Etemadi   10
N 6 hours ago by amirhsz
Source: Iranian TST 2018, second exam day 2, problem 5
Let $\omega$ be the circumcircle of isosceles triangle $ABC$ ($AB=AC$). Points $P$ and $Q$ lie on $\omega$ and $BC$ respectively such that $AP=AQ$ .$AP$ and $BC$ intersect at $R$. Prove that the tangents from $B$ and $C$ to the incircle of $\triangle AQR$ (different from $BC$) are concurrent on $\omega$.

Proposed by Ali Zamani, Hooman Fattahi
10 replies
Etemadi
Apr 17, 2018
amirhsz
6 hours ago
high school maths
aothatday   1
N Today at 4:24 PM by waterbottle432
Source: my creation
find $f:\mathbb{R} \rightarrow \mathbb{R}$ such that:
$(x-y)(f(x)+f(y)) \leq f(x^2-y^2)$
1 reply
aothatday
Today at 2:27 PM
waterbottle432
Today at 4:24 PM
k How to pronounce Rusczyk
Dream9   22
N Mar 31, 2025 by MathNinja9
I've always said like ruzz icks. I don't know why I say it as plural but does anyone know how to say the sigma's last name?
22 replies
Dream9
Mar 29, 2025
MathNinja9
Mar 31, 2025
How to pronounce Rusczyk
G H J
G H BBookmark kLocked kLocked NReply
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Dream9
78 posts
#1 • 2 Y
Y by DhruvJha, RainbowJessa
I've always said like ruzz icks. I don't know why I say it as plural but does anyone know how to say the sigma's last name?
Z Y
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jkim0656
533 posts
#2 • 1 Y
Y by RainbowJessa
i say ruzz ick without the plural
and have heard people say it like that too
Z Y
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KF329
297 posts
#3 • 1 Y
Y by RainbowJessa
i just like don't say it but if i have to i also say it like ruzz ick
Z Y
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K1mchi_
6 posts
#4 • 1 Y
Y by RainbowJessa
Rush KUH zick
But tbh im not sure.
Is this post spam or smth?
Z Y
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DhruvJha
806 posts
#5
Y by
roosk-zik
Z Y
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Yihangzh
605 posts
#6 • 2 Y
Y by peppermint_cat, Exponent11
rus-ick$     $
Z Y
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mdk2013
562 posts
#7 • 1 Y
Y by Exponent11
I heard richard RUCH-ick somewhere, i also say rus-ick if people give me weird glances
Z Y
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SpeedCuber7
1766 posts
#8 • 3 Y
Y by mdk2013, sehgalsh, Exponent11
The official Wikipedia article gives the pronounciation as /ˈrʌsɪk/ or $\boxed{\text{ruh-ssik}}$ $\blacksquare$.
Z Y
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snake2020
4479 posts
#9
Y by
QED.$    $
Z Y
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vincentwant
1283 posts
#10
Y by
in Polish it's similar to "ruschik" with rolled r and english long u and short i
This post has been edited 2 times. Last edited by vincentwant, Mar 31, 2025, 12:36 AM
Z Y
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DhruvJha
806 posts
#11 • 1 Y
Y by Exponent11
vincentwant wrote:
in Polish it's similar to "ruschik" with rolled r and english long u and short i

Yeah that seems right

However when referring to him, I just say Richard
This post has been edited 1 time. Last edited by DhruvJha, Mar 31, 2025, 12:43 AM
Reason: sw
Z Y
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mathenrichmentaops
534 posts
#12
Y by
roos-chik
Z Y
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avyaank
48 posts
#13 • 1 Y
Y by Exponent11
rus-zik


weee
Z Y
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km2
2 posts
#14
Y by
czyk makes like a check or chick sound I think so maybe Rus-chick or Rus-check?
Z Y
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km2
2 posts
#15
Y by
My friend's last name is Tomczyk and its Tom-chick
Z Y
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WiseHawkCuteFriendly
565 posts
#16
Y by
I say Russ Zyuck for some reason
Z Y
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KF329
297 posts
#17
Y by
eh...but anyway

farewell, Richard Rusczyk
Z Y
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K1mchi_
6 posts
#18
Y by
I apologize, my previous post was a joke.

The cyk part is something like check or chick.
Z Y
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MathNinja9
2669 posts
#19
Y by
I just say "RUSC-zick" :rotfl: :P
Z Y
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Yrock
1245 posts
#20
Y by
rooh-zeek

with a long u
This post has been edited 1 time. Last edited by Yrock, Mar 31, 2025, 4:57 PM
Z Y
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MrMustache
2923 posts
#21
Y by
rooz check is the correct pronunciation I believe
Z Y
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Dream9
78 posts
#22 • 2 Y
Y by MathNinja9, Exponent11
At least there's Richard :)
Z Y
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MathNinja9
2669 posts
#23
Y by
Dream9 wrote:
At least there's Richard :)

yessss so much easier :rotfl:
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