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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 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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super duper ez radax problem
iStud   8
N 37 minutes ago by MathsII-enjoy
Source: Monthly Contest KTOM March 2025 P1 Essay
Given an acute triangle $ABC$ with $BC<AB<AC$. Points $D$ and $E$ are on $AB$ and $AC$ respectively such that $DB=BC=CE$. Lines $CD$ and $BE$ meet at $F$. $I$ is the incenter of $\triangle{ABC}$ and $H$ is the orthocenter of $\triangle{DEF}$. $\omega_b$ and $\omega_c$ are circles with diameter $BD$ and $CE$, respectively, intersecting each other at points $X$ and $Y$. Prove that $I$ and $H$ lie on $XY$.

Hint
8 replies
iStud
Mar 18, 2025
MathsII-enjoy
37 minutes ago
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Cyclic ine
m4thbl3nd3r   5
N 37 minutes ago by sqing
Let $a,b,c>0$ such that $a+b+c=3$. Prove that $$a^3b+b^3c+c^3a+9abc\le 12$$
5 replies
m4thbl3nd3r
Yesterday at 3:17 PM
sqing
37 minutes ago
J
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Points in general position
AshAuktober   2
N an hour ago by Bata325
Source: 2025 Nepal ptst p1 of 4
Shining tells Prajit a positive integer $n \ge 2025$. Prajit then tries to place n points such that no four points are concyclic and no $3$ points are collinear in Euclidean plane, such that Shining cannot find a group of three points such that their circumcircle contains none of the other remaining points. Is he always able to do so?

(Prajit Adhikari, Nepal and Shining Sun, USA)
2 replies
AshAuktober
Mar 15, 2025
Bata325
an hour ago
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Transitive relation
MetaphysicalWukong   0
an hour ago
Source: Huabing Dai
Let ? be the relation on the set of integers, where (?, ?) ∈ ? if ? + ? is even.
Is ? transitive?

I know ? is reflexive and symmetric but not sure about transitivity.
0 replies
MetaphysicalWukong
an hour ago
0 replies
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Interesting inequality
sqing   1
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0,(ab+c)(ac+b)\neq 0 $ and $ a+b+c=3 . $ Prove that
$$ \frac{1}{ab+kc}+\frac{1}{ac+kb} \geq\frac{4}{3k} $$Where $ k\geq 3. $
$$ \frac{1}{ab+2c}+\frac{1}{ac+2b} \geq\frac{16}{25} $$$$ \frac{1}{ab+3c}+\frac{1}{ac+3b} \geq\frac{4}{9} $$$$ \frac{1}{ab+4c}+\frac{1}{ac+4b} \geq\frac{1}{3} $$

1 reply
sqing
an hour ago
sqing
an hour ago
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Problem 2
delegat   145
N an hour ago by Marcus_Zhang
Source: 0
Let $n\ge 3$ be an integer, and let $a_2,a_3,\ldots ,a_n$ be positive real numbers such that $a_{2}a_{3}\cdots a_{n}=1$. Prove that
\[(1 + a_2)^2 (1 + a_3)^3 \dotsm (1 + a_n)^n > n^n.\]

Proposed by Angelo Di Pasquale, Australia
145 replies
delegat
Jul 10, 2012
Marcus_Zhang
an hour ago
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CMJ 1284 (Crazy Concyclic Circumcenter Circus)
kgator   0
an hour ago
Source: College Mathematics Journal Volume 55 (2024), Issue 4: https://doi.org/10.1080/07468342.2024.2373015
1284. Proposed by Tran Quang Hung, High School for Gifted Students, Vietnam National University, Hanoi, Vietnam. Let quadrilateral $ABCD$ not be a trapezoid such that there is a circle centered at $I$ that is tangent to the four sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$. Let $X$, $Y$, $Z$, and $W$ be the circumcenters of the triangles $IAB$, $IBC$, $ICD$, and $IDA$, respectively. Prove that there is a circle containing the circumcenters of the triangles $XAB$, $YBC$, $ZCD$, and $WDA$.
0 replies
kgator
an hour ago
0 replies
J
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euler-totient function
Laan   3
N an hour ago by top1vien
Proof that there are infinitely many positive integers $n$ such that
$\varphi(n)<\varphi(n+1)<\varphi(n+2)$
3 replies
Laan
Friday at 7:13 AM
top1vien
an hour ago
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Loop of Logarithms
scls140511   12
N an hour ago by yyhloveu1314
Source: 2024 China Round 1 (Gao Lian)
Round 1

1 Real number $m>1$ satisfies $\log_9 \log_8 m =2024$. Find the value of $\log_3 \log_2 m$.
12 replies
scls140511
Sep 8, 2024
yyhloveu1314
an hour ago
J
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A cyclic inequality
JK1603JK   1
N 2 hours ago by jokehim
Source: unknown
Let a,b,c be real numbers. Prove that a^6+b^6+c^6\ge 2(a+b+c)(ab+bc+ca)(a-b)(b-c)(c-a).
1 reply
JK1603JK
3 hours ago
jokehim
2 hours ago
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bank accounts
cloventeen   1
N 2 hours ago by jkim0656
edgar has three bank accounts, each with an integer amount of dollars in it. He is only allowed to transfer money from one account to another if, by doing so, the latter ends up with double the money it had previously. Prove that edgar can always transfer all of his money into two accounts. Will he always be able to transfer all of his money into a single account?
1 reply
cloventeen
2 hours ago
jkim0656
2 hours ago
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Divisibility
RenheMiResembleRice   0
2 hours ago
Source: Byer
Prove that for all n ∈ ℕ, 133|($11^{\left(n+2\right)}+12^{\left(2n+1\right)}$).
0 replies
RenheMiResembleRice
2 hours ago
0 replies
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2 var inquality
sqing   3
N 2 hours ago by sqing
Source: Own
Let $ a,b>0 $ and $ 3a+4b=a^3b^2. $ Prove that
$$2a+b+\dfrac{2}{a}+\dfrac{3}{b}\geq \frac{11}{\sqrt2}$$$$a+\dfrac{2}{a}+\dfrac{3}{b}\geq 4\sqrt[4]{\frac23}$$$$\dfrac{2}{a}+\dfrac{3}{b}\geq 2\sqrt[4]3$$$$3a+\dfrac{2}{a}+\dfrac{3}{b}\geq \sqrt[4]{354+66\sqrt{33}}$$
3 replies
sqing
Mar 4, 2025
sqing
2 hours ago
J
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Tangent.
steven_zhang123   1
N 2 hours ago by ehuseyinyigit
Source: China TST 2001 Quiz 6 P1
In \( \triangle ABC \) with \( AB > BC \), a tangent to the circumcircle of \( \triangle ABC \) at point \( B \) intersects the extension of \( AC \) at point \( D \). \( E \) is the midpoint of \( BD \), and \( AE \) intersects the circumcircle of \( \triangle ABC \) at \( F \). Prove that \( \angle CBF = \angle BDF \).
1 reply
steven_zhang123
2 hours ago
ehuseyinyigit
2 hours ago
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J
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sum of divisors nt
Soupboy0   0
Friday at 2:47 PM
Source: own
Show that $\sum_{i=1}^{n} (\sigma(i)+n\pmod {i}) = n^2$, where $\sigma(k)$ denotes the sum of the factors of $k$.
0 replies
Soupboy0
Friday at 2:47 PM
0 replies
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sum of divisors nt
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sum of divisors
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Soupboy0
164 posts
Soupboy0
#1 h  Friday at 2:47 PM
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Show that $\sum_{i=1}^{n} (\sigma(i)+n\pmod {i}) = n^2$, where $\sigma(k)$ denotes the sum of the factors of $k$.
This post has been edited 4 times. Last edited by Soupboy0, Yesterday at 7:02 PM
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