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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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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
Find the marginal profit..
ArmiAldi   1
N 27 minutes ago by Juno_34
Source: can someone help me
The total profit selling x units of books is P(x) = (6x - 7)(9x - 8) .
Find the marginal average profit function?
1 reply
ArmiAldi
Mar 2, 2008
Juno_34
27 minutes ago
Marginal Profit
NC4723   1
N 39 minutes ago by Juno_34
Please help me solve this
1 reply
NC4723
Dec 11, 2015
Juno_34
39 minutes ago
Sequence
Titibuuu   2
N an hour ago by Tkn
Let \( a_1 = a \), and for all \( n \geq 1 \), define the sequence \( \{a_n\} \) by the recurrence
\[
a_{n+1} = a_n^2 + 1
\]Prove that there is no natural number \( n \) such that
\[
\prod_{k=1}^{n} \left( a_k^2 + a_k + 1 \right)
\]is a perfect square.
2 replies
Titibuuu
Today at 2:22 AM
Tkn
an hour ago
Combinatorics
imnotgoodatmathsorry   0
an hour ago
Source: By @irregular22104
Given two positive integers $a,b$ written on the board. We apply the following rule: At each step, we will add all the numbers that are the sum of the two numbers on the board so that the sum does not appear on the board. For example, if the two initial numbers are $2,5$; then the numbers on the board after step 1 are $2,5,7$; after step 2 are $2,5,7,9,12;...$
1) With $a = 3$; $b = 12$, prove that the number 2024 cannot appear on the board.
2) With $a = 2$; $b = 34$, prove that the number 2024 can appear on the board.
0 replies
imnotgoodatmathsorry
an hour ago
0 replies
Iranian geometry configuration
Assassino9931   0
an hour ago
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
0 replies
Assassino9931
an hour ago
0 replies
Inequality, inequality, inequality...
Assassino9931   0
an hour ago
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
0 replies
Assassino9931
an hour ago
0 replies
Prime sums of pairs
Assassino9931   0
an hour ago
Source: Al-Khwarizmi Junior International Olympiad 2025 P5
Sevara writes in red $8$ distinct positive integers and then writes in blue the $28$ sums of each two red numbers. At most how many of the blue numbers can be prime?

Marin Hristov, Bulgaria
0 replies
Assassino9931
an hour ago
0 replies
help me solve this problem. Thanks
tnhan.129   0
an hour ago
Find f:R+ -> R such that:
(x+1/x).f(y) = f(xy) + f(y/x)
0 replies
tnhan.129
an hour ago
0 replies
Line passing through orthocenter
pokmui9909   4
N an hour ago by Tkn
Source: KMO 2024 P7
In an acute triangle $ABC$, let a line $\ell$ pass through the orthocenter and not through point $A$. The line $\ell$ intersects line $BC$ at $P(\neq B, C)$. A line passing through $A$ and perpendicular to $\ell$ meets the circumcircle of triangle $ABC$ at $R(\neq A)$. Let the feet of the perpendiculars from $A, B$ to $\ell$ be $A', B'$, respectively. Define line $\ell_1$ as the line passing through $A'$ and perpendicular to $BC$, and line $\ell_2$ as the line passing through $B'$ and perpendicular to $CA$. Prove that if $Q$ is the reflection of the intersection of $\ell_1$ and $\ell_2$ across $\ell$, then $\angle PQR = 90^{\circ}$.
4 replies
pokmui9909
Nov 9, 2024
Tkn
an hour ago
Inequality with number of divisors
MathLuis   12
N an hour ago by Grasshopper-
Source: Iberoamerican MO 2024 Day 1 P1
For each positive integer $n$, let $d(n)$ be the number of positive integer divisors of $n$.
Prove that for all pairs of positive integers $(a,b)$ we have that:
\[ d(a)+d(b) \le d(\gcd(a,b))+d(\text{lcm}(a,b)) \]and determine all pairs of positive integers $(a,b)$ where we have equality case.
12 replies
MathLuis
Sep 21, 2024
Grasshopper-
an hour ago
No three collinear
USJL   1
N 2 hours ago by Photaesthesia
Source: 2025 Taiwan TST Round 3 Mock P6
Given a positive integer $n\geq 3$. A convex polygon is said to be $n$-good if it contains $n$ lattice points where any three of them are not collinear.

(a) Show that there exists an $n$-good convex polygon with area at most $4n^2$.
(b) Show that there exists a constant $c>0$ so that any $n$-good convex polygon has area at least $cn^2$.

Proposed by usjl
1 reply
USJL
Apr 26, 2025
Photaesthesia
2 hours ago
Concentric Circles
MithsApprentice   61
N 2 hours ago by endless_abyss
Source: USAMO 1998
Let ${\cal C}_1$ and ${\cal C}_2$ be concentric circles, with ${\cal C}_2$ in the interior of ${\cal C}_1$. From a point $A$ on ${\cal C}_1$ one draws the tangent $AB$ to ${\cal C}_2$ ($B\in {\cal C}_2$). Let $C$ be the second point of intersection of $AB$ and ${\cal C}_1$, and let $D$ be the midpoint of $AB$. A line passing through $A$ intersects ${\cal C}_2$ at $E$ and $F$ in such a way that the perpendicular bisectors of $DE$ and $CF$ intersect at a point $M$ on $AB$. Find, with proof, the ratio $AM/MC$.
61 replies
MithsApprentice
Oct 9, 2005
endless_abyss
2 hours ago
Romania NMO 2023 Grade 11 P1
DanDumitrescu   15
N 5 hours ago by anudeep
Source: Romania National Olympiad 2023
Determine twice differentiable functions $f: \mathbb{R} \rightarrow \mathbb{R}$ which verify relation

\[
    \left( f'(x) \right)^2 + f''(x) \leq 0, \forall x \in \mathbb{R}.
    \]
15 replies
DanDumitrescu
Apr 14, 2023
anudeep
5 hours ago
Subset Ordered Pairs of {1, 2, ..., 10}
ahaanomegas   11
N 5 hours ago by cappucher
Source: Putnam 1990 A6
If $X$ is a finite set, let $X$ denote the number of elements in $X$. Call an ordered pair $(S,T)$ of subsets of $ \{ 1, 2, \cdots, n \} $ $ \emph {admissible} $ if $ s > |T| $ for each $ s \in S $, and $ t > |S| $ for each $ t \in T $. How many admissible ordered pairs of subsets $ \{ 1, 2, \cdots, 10 \} $ are there? Prove your answer.
11 replies
ahaanomegas
Jul 12, 2013
cappucher
5 hours ago
Inegration stuff, integration bee
Acumlus   8
N Apr 11, 2025 by Silver08
I want to learn how to integrate, I'm a ms student with knowledge about math counts ,amc 10 even tho that want help mebut I don't want to dwell in calc, I just want to learn how to integrate and nothing else like I don't want to study it deep, how can I learn how to integrate its for an integration bee hosted near me its a state uni and I want to join so in the span of 2 months how can I learn to integrate without learning calc like fully
8 replies
Acumlus
Apr 7, 2025
Silver08
Apr 11, 2025
Inegration stuff, integration bee
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G H BBookmark kLocked kLocked NReply
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Acumlus
17 posts
#1
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I want to learn how to integrate, I'm a ms student with knowledge about math counts ,amc 10 even tho that want help mebut I don't want to dwell in calc, I just want to learn how to integrate and nothing else like I don't want to study it deep, how can I learn how to integrate its for an integration bee hosted near me its a state uni and I want to join so in the span of 2 months how can I learn to integrate without learning calc like fully
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paxtonw
35 posts
#2
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Do you understand differentiation? You most likely won't be able to understand intergration without first understanding differentiation.
Z K Y
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snake2020
4509 posts
#3
Y by
"Acumlus"
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Acumlus
17 posts
#4
Y by
paxtonw wrote:
Do you understand differentiation? You most likely won't be able to understand intergration without first understanding differentiation.

ill try to learn differentiation, how should I approach this like learning how to integrate
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Acumlus
17 posts
#5
Y by
snake2020 wrote:
"Acumlus"

it was a typo, don't mind the you know what part
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paxtonw
35 posts
#6
Y by
Acumlus wrote:
paxtonw wrote:
Do you understand differentiation? You most likely won't be able to understand intergration without first understanding differentiation.

ill try to learn differentiation, how should I approach this like learning how to integrate

Khan Acedamty
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Acumlus
17 posts
#7
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thx , bump
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HacheB2031
394 posts
#8
Y by
You should learn differentiation because:
1. Differentiation is easier than indefinite integration.
2. It has many interesting properties, particularly extrema and MVT.
3. The Fundamental Theorem of Calculus links differentiation and integration.
4. Most integration tricks rely on differentiation because of derivative rules.
Try to learn how to differentiate first.
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Silver08
460 posts
#9 • 1 Y
Y by paxtonw
You should definitely learn differentiation first!!

1. Learn the concept of Differentiation rules!! Watch from this Youtube Channel: PatrickJMT
2. Practice differentiation with example problems!! Watch from this Youtube Channel: OrganicChemistryTutor
After that, apply the same procedure for integral concepts: learn first from PatrickJMT, then practice problems from OrganicChemistryTutor.

Then after all that, once your confident and comfortable enough....you can join the dark side :evilgrin:
I have an "integration bee training" series on Youtube which is easy to find, and I made a book for Integration Bee Problem Writers:
https://artofproblemsolving.com/community/c1967976h3218725

I wish you the best of luck!!!
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