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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.

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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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9 ARML Location
deduck   40
N 12 minutes ago by zhenghua
UNR -> Nevada
St Anselm -> New Hampshire
PSU -> Pennsylvania
WCU -> North Carolina


Put your USERNAME in the list ONLY IF YOU WANT TO!!!! !!!!!

I'm going to UNR if anyone wants to meetup!!! :D

Current List:
Iowa
UNR
PSU
St Anselm
WCU
40 replies
deduck
May 6, 2025
zhenghua
12 minutes ago
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Inequality, inequality, inequality...
Assassino9931   6
N 16 minutes ago by NO_SQUARES
Source: Al-Khwarizmi Junior International Olympiad 2025 P6
Let $a,b,c$ be real numbers such that \[ab^2+bc^2+ca^2=6\sqrt{3}+ac^2+cb^2+ba^2.\]Find the smallest possible value of $a^2 + b^2 + c^2$.

Binh Luan and Nhan Xet, Vietnam
6 replies
+1 w
Assassino9931
5 hours ago
NO_SQUARES
16 minutes ago
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inequality involving GCD and square roots
gaussious   1
N 18 minutes ago by Lil_flip38
how to even approach this?
1 reply
gaussious
4 hours ago
Lil_flip38
18 minutes ago
J
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f(f(x+y)) = f(x)+f(y)
NamelyOrange   3
N 24 minutes ago by jasperE3
Source: Evan's FE handout
Find all continuous $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f(f(x+y)) = f(x)+f(y)$ for all real $x,y$.
3 replies
1 viewing
NamelyOrange
Mar 14, 2025
jasperE3
24 minutes ago
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IMO Shortlist 2010 - Problem N3
Amir Hossein   30
N 24 minutes ago by cj13609517288
Find the smallest number $n$ such that there exist polynomials $f_1, f_2, \ldots , f_n$ with rational coefficients satisfying \[x^2+7 = f_1\left(x\right)^2 + f_2\left(x\right)^2 + \ldots + f_n\left(x\right)^2.\]

Proposed by Mariusz Skałba, Poland
30 replies
Amir Hossein
Jul 17, 2011
cj13609517288
24 minutes ago
J
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help me solve this problem. Thanks
tnhan.129   1
N 27 minutes ago by jasperE3
Find f:R+ -> R such that:
(x+1/x).f(y) = f(xy) + f(y/x)
1 reply
tnhan.129
5 hours ago
jasperE3
27 minutes ago
J
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Iranian geometry configuration
Assassino9931   1
N 40 minutes ago by sami1618
Source: Al-Khwarizmi Junior International Olympiad 2025 P7
Let $ABCD$ be a cyclic quadrilateral with circumcenter $O$, such that $CD$ is not a diameter of its circumcircle. The lines $AD$ and $BC$ intersect at point $P$, so that $A$ lies between $D$ and $P$, and $B$ lies between $C$ and $P$. Suppose triangle $PCD$ is acute and let $H$ be its orthocenter. The points $E$ and $F$ on the lines $BC$ and $AD$, respectively, are such that $BD \parallel HE$ and $AC\parallel HF$. The line through $E$, perpendicular to $BC$, intersects $AD$ at $L$, and the line through $F$, perpendicular to $AD$, intersects $BC$ at $K$. Prove that the points $K$, $L$, $O$ are collinear.

Amir Parsa Hosseini Nayeri, Iran
1 reply
Assassino9931
5 hours ago
sami1618
40 minutes ago
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Interesting inequalities
sqing   0
40 minutes ago
Source: Own
Let $ a,b,c\geq 0 , (5a+2)(b+c)=7.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{19}{11}$$Let $ a,b,c\geq 0 , (20a+7)(b+c)=27.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{69}{41}$$Let $ a,b,c\geq 0 , (50a+17)(b+c)=67.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{169}{101}$$Let $ a,b,c\geq 0 , (2a+1)(b+c)=3.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq4(\sqrt{6}- 2)$$Let $ a,b,c\geq 0 , (5a+3)(b+c)=8.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq2\sqrt{10}- \frac{9}{2}$$
0 replies
sqing
40 minutes ago
0 replies
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Is the result of this is the same as cauchy?
ItzsleepyXD   1
N 42 minutes ago by maromex
Source: curiosity
Prove or disprove that for all continuous or monotonic function $f : \mathbb{R}^2 \to \mathbb{R}$ .The solution to $$f(a,x)+f(b,y)=f(a+b,x+y) \text{ for all }a,b,x,y \in \mathbb{R}$$is only $f(x,y)=cx+dy$ for some $c,d \in \mathbb{R}$
1 reply
ItzsleepyXD
3 hours ago
maromex
42 minutes ago
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Fake number theory
Davdav1232   4
N an hour ago by NO_SQUARES
Source: Israel TST p1
For a positive integer \( n \geq 2 \), does there exist positive integer solutions to the following system of equations?

\[ \begin{cases} a^n - 2b^n = 1, \\ b^n - 2c^n = 1. \end{cases} \]
4 replies
Davdav1232
Dec 19, 2024
NO_SQUARES
an hour ago
J
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Interesting inequalities
sqing   1
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0 , (a+k )(b+c)=k+1.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2k-3+2\sqrt{k+1}}{3k-1}$$Where $ k\geq \frac{2}{3}.$
Let $ a,b,c\geq 0 , (a+1)(b+c)=2.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq 2\sqrt{2}-1$$Let $ a,b,c\geq 0 , (a+3)(b+c)=4.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{7}{4}$$Let $ a,b,c\geq 0 , (3a+2)(b+c)= 5.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2(2\sqrt{15}-5)}{3}$$
1 reply
sqing
an hour ago
sqing
an hour ago
J
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9 Will I make JMO?
EaZ_Shadow   15
N an hour ago by orangebear
will I be able to make it... will the cutoffs will be pre-2024
15 replies
EaZ_Shadow
Feb 7, 2025
orangebear
an hour ago
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Past USAMO Medals
sdpandit   1
N 2 hours ago by CatCatHead
Does anyone know where to find lists of USAMO medalists from past years? I can find the 2025 list on their website, but they don't seem to keep lists from previous years and I can't find it anywhere else. Thanks!
1 reply
sdpandit
Thursday at 7:44 PM
CatCatHead
2 hours ago
J
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An FE. Who woulda thunk it?
nikenissan   116
N 6 hours ago by anudeep
Source: 2021 USAJMO Problem 1
Let $\mathbb{N}$ denote the set of positive integers. Find all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for positive integers $a$ and $b,$ \[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]
116 replies
nikenissan
Apr 15, 2021
anudeep
6 hours ago
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amc 10 cooked
PaperMath   119
N Apr 10, 2025 by gamerlegend
Guys any tips to staying calm? (please don't reply with take a deep breath)
119 replies
PaperMath
Nov 5, 2024
gamerlegend
Apr 10, 2025
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amc 10 cooked
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Reveal topic tags
AMC 10
cooked
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jb2015007
1948 posts
jb2015007
#115 h  Jan 7, 2025, 4:55 PM
Y by
by playing FTW
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PikaPika999
1759 posts
PikaPika999
#116 h  Jan 7, 2025, 5:21 PM
Y by
play some intense video games! :ddr:
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Tennis_Coke_Life
65 posts
Tennis_Coke_Life
#117 h  Jan 7, 2025, 8:42 PM • 1 Y
Y by PikaPika999
Scilyse wrote:
unethical tip: don't sleep before the test so that time seems to go slower during the test giving you more time to think about the questions

this is next level stuff
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Dolphincurious79
543 posts
Dolphincurious79
#118 h  Jan 7, 2025, 9:01 PM • 1 Y
Y by PikaPika999
read a book peacefully
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PikaPika999
1759 posts
PikaPika999
#119 h  Jan 7, 2025, 11:34 PM
Y by
Tennis_Coke_Life wrote:
Scilyse wrote:
unethical tip: don't sleep before the test so that time seems to go slower during the test giving you more time to think about the questions

this is next level stuff

nah that's actually crazy :rotfl: wait a minute, that actually seems like it might work! yk what? Ima actually do that! :D
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1220118
10 posts
1220118
#120 h  Jan 7, 2025, 11:44 PM • 2 Y
Y by PaperMath, jlcong
jlcong wrote:
In ftw I can never pull out a win? How to gain speed?

Touch grass
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rohan3142
11 posts
rohan3142
#121 h  Jan 18, 2025, 7:20 PM
Y by
Listen to classical music before the test but not Mahler otherwise ur cooked...
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Scilyse
387 posts
Scilyse
#122 h  Jan 21, 2025, 4:42 PM
Y by
nah mahler is fine, i recommend mahler 8
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anticodon
160 posts
anticodon
#123 h  Jan 22, 2025, 6:23 PM
Y by
rohan3142 wrote:
Listen to classical music before the test but not Mahler otherwise ur cooked...

as long as you're not playing or have played that piece you're fine
just dont get it stuck in your head
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erik54321
54 posts
erik54321
#124 h  Jan 22, 2025, 7:22 PM
Y by
fail the test . . . as easy as that
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guineapig2013
1770 posts
guineapig2013
#125 h  Jan 22, 2025, 8:16 PM
Y by
erik54321 wrote:
fail the test . . . as easy as that

Wow so inspirational
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fastgoodboy
359 posts
fastgoodboy
#126 h  Mar 6, 2025, 1:14 AM
Y by
Play some super satisfying games
Z K Y
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LostRiptide
29 posts
LostRiptide
#127 h  Mar 6, 2025, 1:46 AM
Y by
willale30 wrote:
Mindfulness and Meditation.
Listen to Music.

Idk about you but I would argue never listen to music, game, etc before a test
This post has been edited 1 time. Last edited by LostRiptide, Mar 6, 2025, 1:47 AM
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parnikap
296 posts
parnikap
#128 h  Apr 10, 2025, 12:36 AM
Y by
LostRiptide wrote:
willale30 wrote:
Mindfulness and Meditation.
Listen to Music.

Idk about you but I would argue never listen to music, game, etc before a test

wait why though
its kind of calming and puts me in a semi-chill headspace
though i do understand it can be different for different people
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gamerlegend
2 posts
gamerlegend
#129 h  Apr 10, 2025, 4:43 PM
Y by
everyone has this issue i think best way is to just remember that it's just a contst
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