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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
J
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Time to bring it on!
giangtruong13   0
27 minutes ago
Source: New probs
Prove that the equation $$x^2+y^2-z^2+2=xyz$$has no integer solutions
0 replies
giangtruong13
27 minutes ago
0 replies
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JBMO Shortlist 2020 N4
Lukaluce   5
N 29 minutes ago by MITDragon
Source: JBMO Shortlist 2020
Find all prime numbers $p$ such that

$(x + y)^{19} - x^{19} - y^{19}$

is a multiple of $p$ for any positive integers $x$, $y$.
5 replies
Lukaluce
Jul 4, 2021
MITDragon
29 minutes ago
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Diferential ecuation from physics
QQQ43   1
N 37 minutes ago by QQQ43
Find all functions f:R -> R such that :
f''(x)+f'(x)*b+cos(f(x))*c=a ; where a,b,c are constants in R
f'(0)=0
f(0)=0
1 reply
QQQ43
Yesterday at 2:10 PM
QQQ43
37 minutes ago
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Inspired by JK1603JK
sqing   1
N an hour ago by sqing
Source: Own
Let $ a,b\geq 0 $ and $ a^2+ab+b^2+a+b=5. $ Prove that
$$\frac{ (a+b)(ab+1)}{a+b+1} \leq \frac{4}{3}$$$$ \frac{(a+b)(ab+1)}{a+b+ab-1}\leq \frac{9+\sqrt{21}}{6}$$$$\frac{a^2b+b^2+a }{a+b } \leq \frac{\sqrt{21}-1}{2}$$$$\frac{a^2b+b^2+a+b}{a+b+1} \leq \frac{\sqrt{21}-1}{2}$$
1 reply
sqing
an hour ago
sqing
an hour ago
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Abelkonkurransen 2025 3a
Lil_flip38   4
N an hour ago by Lil_flip38
Source: abelkonkurransen
Let \(ABC\) be a triangle. Let \(E,F\) be the feet of the altitudes from \(B,C\) respectively. Let \(P,Q\) be the projections of \(B,C\) onto line \(EF\). Show that \(PE=QF\).
4 replies
1 viewing
Lil_flip38
4 hours ago
Lil_flip38
an hour ago
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postaffteff
JetFire008   15
N an hour ago by JetFire008
Source: Internet
Let $P$ be the Fermat point of a $\triangle ABC$. Prove that the Euler line of the triangles $PAB$, $PBC$, $PCA$ are concurrent and the point of concurrence is $G$, the centroid of $\triangle ABC$.
15 replies
JetFire008
Mar 15, 2025
JetFire008
an hour ago
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MTRP Subjective P2.2(Seniors)
sanyalarnab   1
N an hour ago by anudeep
Source: Paper
In the planet of MTRPia, one alien named Bob wants to build roads across all the cities all over the planet. The alien government has imposed the condition that this construction must be carried out in such a way so that one can go from one city to any other city through the network of roads thus constructed. To have consistency in the whole process, Bob decides to have an even number of lords originating from each city. Prove that starting from an arbitrary city one can traverse the whole network of roads without ever traversing the same road twice.
1 reply
sanyalarnab
Mar 20, 2024
anudeep
an hour ago
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(x-2y)/y + (2y-4)/x + 4/xy = 0 and 1/x + 1/y+ 1/z =2
parmenides51   2
N an hour ago by ali123456
Source: Greece JBMO TST 2010 p2
Find all real $x,y,z$ such that $\frac{x-2y}{y}+\frac{2y-4}{x}+\frac{4}{xy}=0$ and $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2$.
2 replies
parmenides51
Apr 29, 2019
ali123456
an hour ago
J
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Forgotten number theory
giangtruong13   0
an hour ago
Source: Forgotten forum
Solve in $\mathbb{N}$ \[ x^3+y^3+z^3=4^n\cdot{n^3} \]
0 replies
giangtruong13
an hour ago
0 replies
J
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if a^2+b^2+c^2+d^2=4 and a,b,c,d > 0 prove 2 of a,b,c,d have sum <=2
parmenides51   12
N an hour ago by ali123456
Source: Greece JBMO TST 2018 p1
Let $a,b,c,d$ be positive real numbers such that $a^2+b^2+c^2+d^2=4$.
Prove that exist two of $a,b,c,d$ with sum less or equal to $2$.
12 replies
parmenides51
Apr 28, 2019
ali123456
an hour ago
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nice limits :D
Levieee   10
N 2 hours ago by Sprion
$\text{nice limit sums}$ :D :play_ball:
10 replies
Levieee
Yesterday at 10:53 PM
Sprion
2 hours ago
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ISI 2024 P1
MrOreoJuice   7
N 2 hours ago by Levieee
Find, with proof, all possible values of $t$ such that
\[\lim_{n \to \infty} \left( \frac{1 + 2^{1/3} + 3^{1/3} + \dots + n^{1/3}}{n^t} \right ) = c\]for some real $c>0$. Also find the corresponding values of $c$.
7 replies
MrOreoJuice
May 12, 2024
Levieee
2 hours ago
J
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Cool NT with Sets and Mod
pear333   1
N 2 hours ago by pear333
Find all integers $a$ such that there exists a set $X$ of $6$ integers satisfying the following condition: for each $k = 1,2,...,36$, there exist $x, y \in X$ such that $ax+y-k$ is divisible by $37$.
1 reply
pear333
Yesterday at 8:18 AM
pear333
2 hours ago
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Differentiation Marathon!
LawofCosine   186
N 5 hours ago by LawofCosine
Hello, everybody!

This is a differentiation marathon. It is just like an ordinary marathon, where you can post problems and provide solutions to the problem posted by the previous user. You can only post differentiation problems (not including integration and differential equations) and please don't make it too hard!

Have fun!

(Sorry about the bad english)
186 replies
LawofCosine
Feb 1, 2025
LawofCosine
5 hours ago
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real analysis
ay19bme   1
N Today at 1:36 AM by alexheinis
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1 reply
ay19bme
Yesterday at 8:10 PM
alexheinis
Today at 1:36 AM
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real analysis
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Reveal topic tags
real analysis
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ay19bme
259 posts
ay19bme
#1 h  Yesterday at 8:10 PM
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alexheinis
10475 posts
alexheinis
#2 h  Today at 1:36 AM • 1 Y
Y by Mathzeus1024
I will write $a$ instead of $\epsilon$ then with $x=at$ we get $\int_0^\infty e^{-t}(\cos 3at+(at)^2+\sqrt{at+4})dt$. We may assume $a\le 1$, then we have the integrable dominating function $e^{-t}(1+t^2+\sqrt{t+4})$. Hence we may apply Lebesgue and we find $3\int_0^\infty e^{-t}dt=3$.
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