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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.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]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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All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
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
MATHCOUNTS
ILOVECATS127   45
N 33 minutes ago by Glowworm
Hi,

I am looking to get on my school MATHCOUNTS team next year in 7th grade, and I had a question: Where do the school round questions come from? (Sprint, Chapter, Team, Countdown)
45 replies
ILOVECATS127
May 7, 2025
Glowworm
33 minutes ago
Some number theory
EeEeRUT   4
N an hour ago by juckter
Source: Thailand MO 2025 P9
Let $p$ be an odd prime and $S = \{1,2,3,\dots, p\}$
Assume that $U: S \rightarrow S$ is a bijection and $B$ is an integer such that $$B\cdot U(U(a)) - a \: \text{ is a multiple of} \: p \: \text{for all} \: a \in S$$Show that $B^{\frac{p-1}{2}} -1$ is a multiple of $p$.
4 replies
EeEeRUT
May 14, 2025
juckter
an hour ago
Simple Geometry
AbdulWaheed   0
2 hours ago
Source: EGMO
Try to avoid Directed angles
Let ABC be an acute triangle inscribed in circle $\Omega$. Let $X$ be the midpoint of the arc $\overarc{BC}$ not containing $A$ and define $Y, Z$ similarly. Show that the orthocenter of $XYZ$ is the incenter $I$ of $ABC$.
0 replies
AbdulWaheed
2 hours ago
0 replies
Graph Theory
ABCD1728   0
2 hours ago
Can anyone provide the PDF version of "Graphs: an introduction" by Radu Bumbacea (XYZ press), thanks!
0 replies
ABCD1728
2 hours ago
0 replies
relay race!
A7456321   8
N 2 hours ago by Craftybutterfly
Welcome to the math relay race! To participate, answer the problem in the latest post, then post one yourself! Please also mark the question number. E.x. if the one before you is question #35, then mark yours as question #36. Easy as pi!

Note: If you choose to help someone with a problem you don't have to make one yourself unless you want to. You are also welcome to ask a question without having to post a new problem. Please do not post a new problem until the previous one is solved. All topics are welcome except for anything >12th grade. Trig is fine. Calculus is not. :D

Question 1: If it takes 5 monkeys 5 days to eat 5 bananas, then how many days will it take for 4 monkeys to eat 4 bananas? (Hint: It's not 4)

Please upvote! :thumbup:

Goal: 100 questions!

Timeline
8 replies
A7456321
5 hours ago
Craftybutterfly
2 hours ago
Number theory for people who love theory
Assassino9931   3
N 2 hours ago by NamelyOrange
Source: Bulgaria RMM TST 2019
Prove that there is no positive integer $n$ such that $2^n + 1$ divides $5^n-1$.
3 replies
Assassino9931
Jul 31, 2024
NamelyOrange
2 hours ago
Interesting inequalities
sqing   0
2 hours ago
Source: Own
Let $ a,b> 0 ,   a+b+a^2+b^2=2.$ Prove that
$$ab+ \frac{k}{a+b+ab} \geq \frac{3-k+(k-1)\sqrt{5}}{2}$$Where $ k\geq 2. $
$$ab+ \frac{2}{a+b+ab} \geq \frac{1+\sqrt{5}}{2}$$$$ab+ \frac{3}{a+b+ab} \geq  \sqrt{5} $$
0 replies
+1 w
sqing
2 hours ago
0 replies
9 How many squares do you have memorized
LXC007   91
N 3 hours ago by valisaxieamc
How many squares have you memorized. I have 1-20

Edit: to clarify i mean positive squares from 1 so if you say ten you mean you memorized the squares 1,2,3,4,5,6,7,8,9 and 10
91 replies
LXC007
May 17, 2025
valisaxieamc
3 hours ago
9 Pythagorean Triples
ZMB038   50
N 3 hours ago by valisaxieamc
Please put some of the ones you know, and try not to troll/start flame wars! Thank you :D
50 replies
ZMB038
May 19, 2025
valisaxieamc
3 hours ago
Stability of Additive Cauchy Equation
doanquangdang   1
N 4 hours ago by jasperE3
Show that if $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfies
$$
|f(x+y)-f(x)-f(y)-x y| \leq \varepsilon\left(|x|^p+|y|^p\right)
$$for some $\varepsilon>0,$ $p \in[0,1)$ and for all $x, y \in \mathbb{R}$, then there exists a unique solution $a: \mathbb{R} \rightarrow \mathbb{R}$ of the functional equation $a(x+y)=$ $a(x)+a(y)$ for all $x, y \in \mathbb{R}$ such that
$$
\left|f(x)-a(x)-\frac{1}{2} x^2\right| \leq \frac{2}{2-2^p} \varepsilon|x|^p
$$for all $x \in \mathbb{R}$.
1 reply
doanquangdang
Aug 16, 2024
jasperE3
4 hours ago
Polynomials with common roots and coefficients
VicKmath7   10
N 4 hours ago by math-olympiad-clown
Source: Balkan MO SL 2020 A3
Let $P(x), Q(x)$ be distinct polynomials of degree $2020$ with non-zero coefficients. Suppose that they have $r$ common real roots counting multiplicity and $s$ common coefficients. Determine the maximum possible value of $r + s$.

Demetres Christofides, Cyprus
10 replies
VicKmath7
Sep 9, 2021
math-olympiad-clown
4 hours ago
Serbian selection contest for the IMO 2025 - P3
OgnjenTesic   1
N 4 hours ago by korncrazy
Source: Serbian selection contest for the IMO 2025
Find all functions $f : \mathbb{Z} \to \mathbb{Z}$ such that:
- $f$ is strictly increasing,
- there exists $M \in \mathbb{N}$ such that $f(x+1) - f(x) < M$ for all $x \in \mathbb{N}$,
- for every $x \in \mathbb{Z}$, there exists $y \in \mathbb{Z}$ such that
\[
            f(y) = \frac{f(x) + f(x + 2024)}{2}.
        \]Proposed by Pavle Martinović
1 reply
OgnjenTesic
Yesterday at 4:06 PM
korncrazy
4 hours ago
Interesting inequalities
sqing   0
4 hours ago
Source: Own
Let $ a,b,c \geq  0 , a+b+c+abc = 4.$ Prove that
$$ a+ab^2+\frac{15}{4}ab^2c^3  \leq \frac{2(100+13\sqrt{13})}{27}$$$$ 2a+ab^2+ 4ab^2c^3\leq \frac{4(68+5\sqrt{10})}{27}$$$$ 3a+ab^2+ \frac{9}{2}ab^2c^3\leq \frac{2(172+7\sqrt{7})}{27}$$$$a+ab^2+ 3.75982ab^2c^3 \leq \frac{2(100+13\sqrt{13})}{27}$$$$ 2a+ab^2+ 4.21981ab^2c^3\leq \frac{4(68+5\sqrt{10})}{27}$$$$ 3a+ab^2+4.73626ab^2c^3\leq \frac{2(172+7\sqrt{7})}{27}$$
0 replies
sqing
4 hours ago
0 replies
Inspired by old results
sqing   0
5 hours ago
Source: Own
Let $ a,b,c \geq  0 , a+b+c+abc = 4.$ Prove that
$$ a+ab+2ab^2c^3  \leq \frac{25}{4}$$$$ 2a+ab+\frac{29}{10}ab^2c^3 \leq 9$$$$3a+ab+4ab^2c^3 \leq \frac{49}{4}$$$$ 2a+ab+2.9746371ab^2c^3 \leq 9$$$$3a+ab+4.062494ab^2c^3 \leq \frac{49}{4}$$
0 replies
sqing
5 hours ago
0 replies
k real math problems
Soupboy0   60
N Apr 18, 2025 by Soupboy0
Ill be posting questions once in a while. Here's the first question:

What fraction of numbers from $1$ to $1000$ have the digit $7$ and are divisible by $3$?
60 replies
Soupboy0
Mar 25, 2025
Soupboy0
Apr 18, 2025
real math problems
G H J
G H BBookmark kLocked kLocked NReply
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Soupboy0
486 posts
#53
Y by
11) Given $\log{7} \approx 0.84509804$, how many digits does $7^{7^{7}}$ have?
This post has been edited 2 times. Last edited by Soupboy0, Apr 9, 2025, 12:34 AM
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maxamc
584 posts
#54
Y by
wolfram alpha
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elizhang101412
1256 posts
#55
Y by
Soupboy0 wrote:
11) Given $\log{7} \approx 0.84509804$, how many digits does $7^{7^{7}}$ have?

Click to reveal hidden text
This post has been edited 1 time. Last edited by elizhang101412, Apr 9, 2025, 2:30 AM
Z Y
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K124659
2645 posts
#56
Y by
according to order of operations, it'd be $823543^7$ not $7^823543$
so that'd be Click to reveal hidden text
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Soupboy0
486 posts
#57
Y by
12) What number under $100000$ has the most factors?
Z Y
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fruitmonster97
2501 posts
#58
Y by
K124659 wrote:
according to order of operations, it'd be $823543^7$ not $7^823543$
so that'd be Click to reveal hidden text

nope, when power towers are stacked we assume to do the top ones first, so $7^{7^7}=7^{(7^7)}$
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Charizard_637
118 posts
#59
Y by
Soupboy0 wrote:
12) What number under $100000$ has the most factors?

Answer

Checking with my best friend (and the most inaccurate tool to ever exist) Google AI Overview I'm correct and Alternative Solution is also a solution with Factor Count factors.
This, @Soupboy0, is why we check if the answer is unambiguous.
This post has been edited 1 time. Last edited by Charizard_637, Apr 15, 2025, 2:24 PM
Reason: e
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iwastedmyusername
176 posts
#60
Y by
Soupboy0 wrote:
12) What number under $100000$ has the most factors?

truly one of the greatest real math problems of all time
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K1mchi_
142 posts
#61
Y by
SpeedCuber7 wrote:
maxamc wrote:
SpeedCuber7 wrote:
not a msm problem

solution

it is msm

intedded solution Click to reveal hidden text

are you sure elementary derivatives are part of the middle school curriculum?

it’s msm not msm curriculum silly silly
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Soupboy0
486 posts
#62
Y by
13) What is the highest power of $3$ that can divide a number in the form $\overline{abcdefghij}$, where each of $(a, b, c, d, e, f, g, h, i, j)$ represents a distinct digit from $0$ to $9$?
Z Y
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SpeedCuber7
1854 posts
#63
Y by
K1mchi_ wrote:
it’s msm not msm curriculum silly silly

breh

the description of the forum is "grades 5-8", sounds like middle school to me!
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K1mchi_
142 posts
#64
Y by
SpeedCuber7 wrote:
K1mchi_ wrote:
it’s msm not msm curriculum silly silly

breh

the description of the forum is "grades 5-8", sounds like middle school to me!

that means the forum is for GRADES 5-8 and nawt CURRICULUM for grades 5-8 silly silly
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maxamc
584 posts
#65
Y by
K1mchi_ wrote:
SpeedCuber7 wrote:
K1mchi_ wrote:
it’s msm not msm curriculum silly silly

breh

the description of the forum is "grades 5-8", sounds like middle school to me!

that means the forum is for GRADES 5-8 and nawt CURRICULUM for grades 5-8 silly silly

Agreed.
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maxamc
584 posts
#67
Y by
Soupboy0 wrote:
13) What is the highest power of $3$ that can divide a number in the form $\overline{abcdefghij}$, where each of $(a, b, c, d, e, f, g, h, i, j)$ represents a distinct digit from $0$ to $9$?

1434 moment

sol using python
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Soupboy0
486 posts
#68
Y by
1434 :gleam: 8907
Z Y
G
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=
a