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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.

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:
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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
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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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Math and AI 4 Girls
mkwhe   9
N 3 minutes ago by fishchips
Hey everyone!

The 2025 MA4G competition is now open!

Apply Here: https://xmathandai4girls.submittable.com/submit


Visit https://www.mathandai4girls.org/ to get started!

Feel free to PM or email mathandai4girls@yahoo.com if you have any questions!
9 replies
mkwhe
Apr 5, 2025
fishchips
3 minutes ago
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Wrong Answers Only Pt.2
MathRook7817   24
N 7 minutes ago by xHypotenuse
Problem: What is the area of a triangle with side lengths 13,14, and 15?
WRONG ANSWERS ONLY!

other one got locked for some reason
24 replies
MathRook7817
3 hours ago
xHypotenuse
7 minutes ago
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Maximum Sum in a Grid
Mathdreams   0
25 minutes ago
Source: 2025 Nepal Mock TST Day 3 Problem 1
Let $m$ and $n$ be positive integers. In an $m \times n$ grid, two cells are considered neighboring if they share a common edge. Kritesh performs the following actions:

1. He begins by writing $0$ in any cell of the grid.
2. He then fills each remaining cell with a non-negative integer such that the absolute difference between the numbers in any two neighboring cells is exactly $1$.

Kritesh aims to fill the grid in a way that maximizes the sum of the numbers written in all the cells. Determine the maximum possible sum that Kritesh can achieve in terms of $m$ and $n$.

(Kritesh Dhakal, Nepal)
0 replies
Mathdreams
25 minutes ago
0 replies
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Hard Functional Equation
yaybanana   1
N 25 minutes ago by Rayanelba
Source: own
Find all functions $f:\mathbb{R} \rightarrow \mathbb{R}$ , s.t :

$f(y^2+x)+f(x+yf(x))=f(y)f(y+x)+f(2x)$

for all $x,y \in \mathbb{R}$
1 reply
yaybanana
5 hours ago
Rayanelba
25 minutes ago
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Don't bite me for this straightforward sequence
Assassino9931   6
N 33 minutes ago by Assassino9931
Source: Bulgaria National Olympiad 2025, Day 1, Problem 1
Determine all infinite sequences $a_1, a_2, \ldots$ of real numbers such that
\[ a_{m^2 + m + n} = a_{m}^2 + a_m + a_n\]for all positive integers $m$ and $n$.
6 replies
Assassino9931
Yesterday at 1:47 PM
Assassino9931
33 minutes ago
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Sets With a Given Property
oVlad   2
N 34 minutes ago by nbasrl
Source: Romania TST 2025 Day 1 P4
Determine the sets $S{}$ of positive integers satisfying the following two conditions:
[list=a]
[*]For any positive integers $a, b, c{}$, if $ab + bc + ca{}$ is in $S$, then so are $a + b + c{}$ and $abc$; and
[*]The set $S{}$ contains an integer $N \geqslant 160$ such that $N-2$ is not divisible by $4$.
[/list]
Bogdan Blaga, United Kingdom
2 replies
oVlad
Today at 2:32 PM
nbasrl
34 minutes ago
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Question
mathprodigy2011   6
N 40 minutes ago by Math-lover1
Can someone help me do this question I am super confused and my answer was wrong.
6 replies
mathprodigy2011
Feb 22, 2025
Math-lover1
40 minutes ago
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2025 MATHCOUNTS State Hub
SirAppel   449
N 42 minutes ago by bluedolphinn36
Previous Years' "Hubs": (2022) (2023) (2024)Please Read

Now that it's April and we're allowed to discuss ...
[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) *
[*]VA: 40 (41 40 40 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 40? 38 38)
[*] PA: 38 (41 40 40 38 38 37 36 36 34 34) *
[*] MD: 37 (43 39 39 37 37 37)
[*] AZ: 36 (40? 39? 39 36)
[*] CT: 36 (44 38 38 36 35 35 34 34 34 33 33)
[*] 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)
[*] NV: 34 (41 38 ?? 34)
[*] WI: 34 (40 37 37 34 35 30 28 29 29 29) *
[*] HI: 32 (35 34 32 32)
[*] 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!
449 replies
SirAppel
Apr 1, 2025
bluedolphinn36
42 minutes ago
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mod 16
Iris Aliaj   4
N an hour ago by Levieee
Source: JBMO 1998
Do there exist 16 three digit numbers, using only three different digits in all, so that the all numbers give different residues when divided by 16?

Bulgaria
4 replies
Iris Aliaj
Jun 22, 2004
Levieee
an hour ago
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Functional Equation:
Omerking   2
N 2 hours ago by jasperE3
Find all functions $f:\mathbb {R}\rightarrow \mathbb {R}$ such that:
$$f(x^2f(x)+f(y))=(f(x))^3+y$$
2 replies
Omerking
Today at 12:55 PM
jasperE3
2 hours ago
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A three-variable functional inequality on non-negative reals
Tintarn   8
N 2 hours ago by jasperE3
Source: Dutch TST 2024, 1.2
Find all functions $f:\mathbb{R}_{\ge 0} \to \mathbb{R}$ with
\[2x^3zf(z)+yf(y) \ge 3yz^2f(x)\]for all $x,y,z \in \mathbb{R}_{\ge 0}$.
8 replies
Tintarn
Jun 28, 2024
jasperE3
2 hours ago
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Integer Divisible by 2^2009 with No Zero Digits
zeta1   1
N 2 hours ago by maromex
Show that there exists a positive integer that has no zero digits and is divisible by 2^2009.
1 reply
zeta1
3 hours ago
maromex
2 hours ago
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mixtilinear incircle geometry
Tuguldur   1
N 3 hours ago by ErTeeEs06
Let $D$, $E$, $F$ on $BC$, $CA$, $AB$ be the touch points of the incircle of $\triangle ABC$. Line $EF$ intersects $(ABC)$ at $X_1$, $X_2$. The incircle of $\triangle ABC$ and $(DX_1X_2)$ intersect again at $Y$ . If $T$ is the tangent point of the $A$−mixtilinear incircle and $(ABC)$, prove that $A$, $Y$, $T$ are collinear.
1 reply
Tuguldur
3 hours ago
ErTeeEs06
3 hours ago
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NT function debut
AshAuktober   3
N 3 hours ago by khan.academy
Source: 2025 Nepal Practice TST 3 P2 of 3; Own
Let $f$ be a function taking in positive integers and outputting nonnegative integers, defined as follows:
$f(m)$ is the number of positive integers $n$ with $n \le m$ such that the equation $$an + bm = m^2 + n^2 + 1$$has an integer solution $(a, b)$.
Find all positive integers $x$ such that$f(x) \ne 0$ and $$f(f(x)) = f(x) - 1.$$Adit Aggarwal, India.
3 replies
AshAuktober
5 hours ago
khan.academy
3 hours ago
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Base Problem
Yummo   4
N Mar 29, 2025 by Aaronjudgeisgoat
For any number N, prove that n in base (n-1) = 11.
For example, 3 in base 2 is 11.
4 replies
Yummo
Mar 24, 2025
Aaronjudgeisgoat
Mar 29, 2025
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Base Problem
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Reveal topic tags
Bases
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Yummo
296 posts
Yummo
#1 h  Mar 24, 2025, 6:26 PM
Y by
For any number N, prove that n in base (n-1) = 11.
For example, 3 in base 2 is 11.
This post has been edited 1 time. Last edited by Yummo, Mar 24, 2025, 6:27 PM
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Bummer12345
130 posts
Bummer12345
#2 h  Mar 24, 2025, 6:34 PM
Y by
sol assuming N is in base 10
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ChaitraliKA
1003 posts
ChaitraliKA
#3 h  Mar 24, 2025, 8:47 PM
Y by
Yummo wrote:
For any number $n$, prove that $n$ in base $(n-1)$ = $11$.
For example, $3$ in base $2$ is $11$.

Let the number $n$ in base $(n-1)$ be $AB$.
In base 10, $n$ would be equal to $A(n-1)+B(1)$, and we know $A=1$ because there is only one multiple of $n-1$ less than $n$.
$n=(1)(n-1)+B(1)$ --> $n=n-1+B$ --> $B=1$
So, $AB_{n-1}=11_{n-1}$
Z K Y
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ilikejam
34 posts
ilikejam
#4 h  Mar 29, 2025, 12:27 AM
Y by
wait what but 4 is not congruent to 11 mod 3
Z K Y
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Aaronjudgeisgoat
856 posts
Aaronjudgeisgoat
#5 h  Mar 29, 2025, 1:26 AM
Y by
ilikejam wrote:
wait what but 4 is not congruent to 11 mod 3

base 3, not mod 3
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