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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.

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.

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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]
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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
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Scores are out for jmo
imagien_bad   126
N a few seconds ago by BS2012
RIP..................
126 replies
+9 w
imagien_bad
Yesterday at 6:10 PM
BS2012
a few seconds ago
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USA(J)MO Statistics Out
BS2012   1
N a few seconds ago by rhydon516
Source: MAA edvistas page
https://maa.edvistas.com/eduview/report.aspx?view=1561&mode=6
who were the 2 usamo perfects
1 reply
+5 w
BS2012
12 minutes ago
rhydon516
a few seconds ago
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URGENT JMO problem 1 Misgrade protest (Cost MOP)
bjump   44
N 6 minutes ago by NoSignOfTheta
I was docked 4 points on jmo 1 and it cost me mop. I got 370 777 and 770 777 got into mop.
This google drive link contains my submission to USAJMO day 1
Day 1 Scans
My solution works except for 2 typos. I wrote bijective instead of non bijective at the end, and i wrote min intead of more specifically minimum over Z. After discussion with vsamc, and megarnie they agreed I should have gotten a 7 on this problem because i demostrated that I knew how to solve it. Is it possible to protest my score, and get into MOP.

Help would be greatly appreciated :surrender:
44 replies
bjump
6 hours ago
NoSignOfTheta
6 minutes ago
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A lot of integer lengths: JMO #6 or USAMO Problem 4
BarbieRocks   81
N an hour ago by lpieleanu
Let $ABC$ be a triangle with $\angle A = 90^{\circ}$. Points $D$ and $E$ lie on sides $AC$ and $AB$, respectively, such that $\angle ABD = \angle DBC$ and $\angle ACE = \angle ECB$. Segments $BD$ and $CE$ meet at $I$. Determine whether or not it is possible for segments $AB$, $AC$, $BI$, $ID$, $CI$, $IE$ to all have integer lengths.
81 replies
BarbieRocks
Apr 29, 2010
lpieleanu
an hour ago
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FE solution too simple?
Yiyj1   9
N 2 hours ago by jasperE3
Source: 101 Algebra Problems from the AMSP
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that the equality $$f(f(x)+y) = f(x^2-y)+4f(x)y$$holds for all pairs of real numbers $(x,y)$.

My solution

I feel like my solution is too simple. Is there something I did wrong or something I missed?
9 replies
Yiyj1
Apr 9, 2025
jasperE3
2 hours ago
J
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interesting function equation (fe) in IR
skellyrah   2
N 2 hours ago by jasperE3
Source: mine
find all function F: IR->IR such that $$ xf(f(y)) + yf(f(x)) = f(xf(y)) + f(xy) $$
2 replies
skellyrah
Today at 9:51 AM
jasperE3
2 hours ago
J
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Complicated FE
XAN4   1
N 2 hours ago by jasperE3
Source: own
Find all solutions for the functional equation $f(xyz)+\sum_{cyc}f(\frac{yz}x)=f(x)\cdot f(y)\cdot f(z)$, in which $f$: $\mathbb R^+\rightarrow\mathbb R^+$
Note: the solution is actually quite obvious - $f(x)=x^n+\frac1{x^n}$, but the proof is important.
Note 2: it is likely that the result can be generalized into a more advanced questions, potentially involving more bash.
1 reply
XAN4
Today at 11:53 AM
jasperE3
2 hours ago
J
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Find all sequences satisfying two conditions
orl   34
N 2 hours ago by YaoAOPS
Source: IMO Shortlist 2007, C1, AIMO 2008, TST 1, P1
Let $ n > 1$ be an integer. Find all sequences $ a_1, a_2, \ldots a_{n^2 + n}$ satisfying the following conditions:
\[ \text{ (a) } a_i \in \left\{0,1\right\} \text{ for all } 1 \leq i \leq n^2 + n; \]

\[ \text{ (b) } a_{i + 1} + a_{i + 2} + \ldots + a_{i + n} < a_{i + n + 1} + a_{i + n + 2} + \ldots + a_{i + 2n} \text{ for all } 0 \leq i \leq n^2 - n. \]
Author: Dusan Dukic, Serbia
34 replies
orl
Jul 13, 2008
YaoAOPS
2 hours ago
J
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IMO Shortlist 2011, G4
WakeUp   125
N 2 hours ago by Davdav1232
Source: IMO Shortlist 2011, G4
Let $ABC$ be an acute triangle with circumcircle $\Omega$. Let $B_0$ be the midpoint of $AC$ and let $C_0$ be the midpoint of $AB$. Let $D$ be the foot of the altitude from $A$ and let $G$ be the centroid of the triangle $ABC$. Let $\omega$ be a circle through $B_0$ and $C_0$ that is tangent to the circle $\Omega$ at a point $X\not= A$. Prove that the points $D,G$ and $X$ are collinear.

Proposed by Ismail Isaev and Mikhail Isaev, Russia
125 replies
WakeUp
Jul 13, 2012
Davdav1232
2 hours ago
J
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Z[x], P(\sqrt[3]5+\sqrt[3]25)=5+\sqrt[3]5
jasperE3   5
N 3 hours ago by Assassino9931
Source: VJIMC 2013 2.3
Prove that there is no polynomial $P$ with integer coefficients such that $P\left(\sqrt[3]5+\sqrt[3]{25}\right)=5+\sqrt[3]5$.
5 replies
jasperE3
May 31, 2021
Assassino9931
3 hours ago
J
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IMO problem 1
iandrei   77
N 3 hours ago by YaoAOPS
Source: IMO ShortList 2003, combinatorics problem 1
Let $A$ be a $101$-element subset of the set $S=\{1,2,\ldots,1000000\}$. Prove that there exist numbers $t_1$, $t_2, \ldots, t_{100}$ in $S$ such that the sets \[ A_j=\{x+t_j\mid x\in A\},\qquad j=1,2,\ldots,100 \] are pairwise disjoint.
77 replies
iandrei
Jul 14, 2003
YaoAOPS
3 hours ago
J
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Divisibility on 101 integers
BR1F1SZ   4
N 3 hours ago by BR1F1SZ
Source: Argentina Cono Sur TST 2024 P2
There are $101$ positive integers $a_1, a_2, \ldots, a_{101}$ such that for every index $i$, with $1 \leqslant i \leqslant 101$, $a_i+1$ is a multiple of $a_{i+1}$. Determine the greatest possible value of the largest of the $101$ numbers.
4 replies
BR1F1SZ
Aug 9, 2024
BR1F1SZ
3 hours ago
J
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2^x+3^x = yx^2
truongphatt2668   2
N 3 hours ago by CM1910
Prove that the following equation has infinite integer solutions:
$$2^x+3^x = yx^2$$
2 replies
truongphatt2668
Yesterday at 3:38 PM
CM1910
3 hours ago
J
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Prove perpendicular
shobber   29
N 3 hours ago by zuat.e
Source: APMO 2000
Let $ABC$ be a triangle. Let $M$ and $N$ be the points in which the median and the angle bisector, respectively, at $A$ meet the side $BC$. Let $Q$ and $P$ be the points in which the perpendicular at $N$ to $NA$ meets $MA$ and $BA$, respectively. And $O$ the point in which the perpendicular at $P$ to $BA$ meets $AN$ produced.

Prove that $QO$ is perpendicular to $BC$.
29 replies
shobber
Apr 1, 2006
zuat.e
3 hours ago
J
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SuMAC Email
miguel00   6
N Apr 6, 2025 by NoSignOfTheta
Did anyone get an email from SuMAC checking availability for summer camp you applied for (residential/online)? I don't know whether it is a good sign or just something that everyone got.
6 replies
miguel00
Apr 2, 2025
NoSignOfTheta
Apr 6, 2025
J
SuMAC Email
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Reveal topic tags
SuMAC
email
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miguel00
592 posts
miguel00
#1 h  Apr 2, 2025, 12:30 AM • 1 Y
Y by PikaPika999
Did anyone get an email from SuMAC checking availability for summer camp you applied for (residential/online)? I don't know whether it is a good sign or just something that everyone got.
Z K Y
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Lhaj3
138 posts
Lhaj3
#2 h  Apr 2, 2025, 12:34 AM • 1 Y
Y by PikaPika999
miguel00 wrote:
Did anyone get an email from SuMAC checking availability for summer camp you applied for (residential/online)? I don't know whether it is a good sign or just something that everyone got.

it means you have been autorejected
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jkim0656
947 posts
jkim0656
#3 h  Apr 2, 2025, 12:38 AM • 1 Y
Y by PikaPika999
Lhaj3 wrote:
miguel00 wrote:
Did anyone get an email from SuMAC checking availability for summer camp you applied for (residential/online)? I don't know whether it is a good sign or just something that everyone got.

it means you have been autorejected

OUCH
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Alex-131
5361 posts
Alex-131
#4 h  Apr 2, 2025, 12:45 AM • 1 Y
Y by PikaPika999
Lhaj3 wrote:
miguel00 wrote:
Did anyone get an email from SuMAC checking availability for summer camp you applied for (residential/online)? I don't know whether it is a good sign or just something that everyone got.

it means you have been autorejected

gg I got the same email too
Z K Y
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AtharvY700
1 post
AtharvY700
#5 h  Apr 6, 2025, 2:31 PM • 1 Y
Y by PikaPika999
why would they only ask the rejected people though? serves them no purpose... only reasonable thing would be to ask everyone or ask only those who got accepted, so that for those accepted cannot make it... their slots would be alloted to someone else
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miguel00
592 posts
miguel00
#6 h  Apr 6, 2025, 3:00 PM • 1 Y
Y by PikaPika999
Lhaj was obviously joking check the date
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NoSignOfTheta
1717 posts
NoSignOfTheta
#7 h  Apr 6, 2025, 4:21 PM • 1 Y
Y by PikaPika999
Everyone got it
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