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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.

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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.
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[*]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!
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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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At least 3 co-prime pairs
eezad3   3
N 2 minutes ago by eezad3
You are given a random permutation of the first $n$ integers where $n>10$. Show that there exists at least three positions $i$ such that $gcd(p[i], p[i+1])=1$ (here $p[i]$ refers to the $i$-th position integer in the permutation)
3 replies
eezad3
Mar 15, 2025
eezad3
2 minutes ago
J
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Functional Equation
AnhQuang_67   0
8 minutes ago
Find all functions $f:\mathbb{R} \to \mathbb{R}$ satisfying: $$f(xf(y)+2y)=f(f(y))+f(xy)+xf(y), \forall x, y \in \mathbb{R}$$
0 replies
AnhQuang_67
8 minutes ago
0 replies
J
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hard......
Noname23   3
N 12 minutes ago by Speedysolver1
problem
3 replies
Noname23
39 minutes ago
Speedysolver1
12 minutes ago
J
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2 var inquality
sqing   0
an hour ago
Source: Own
Let $ a,b $ be nonnegative real numbers such that $ a^2+ab+b^2+a+b=1. $ Prove that
$$ (ab+1)(a+b)\leq \frac{ 20}{27} $$$$ (ab+1)(a+b-1)\leq - \frac{ 10}{27} $$Let $ a,b $ be nonnegative real numbers such that $ a^2+b^2+a+b=1. $ Prove that
$$ (ab+1)(a+b)\leq \frac{ 5\sqrt 3-7}{2} $$$$ (ab+1)(a+b-1)\leq 3\sqrt 3- \frac{ 11}{2} $$
0 replies
sqing
an hour ago
0 replies
J
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Thanks u!
Ruji2018252   0
an hour ago
Find all f: R->R and
\[2^{xy}f(xy-1)+2^{x+y+1}f(x)f(y)=4xy-2,\forall x,y\in\mathbb{R}\]
0 replies
2 viewing
Ruji2018252
an hour ago
0 replies
J
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Inequality with x, y
bel.jad5   6
N an hour ago by sqing
Source: Own
Let x and y positive real numbers such that: $x^2+y^2+xy=3$. Find the maximum of $x^2y$
6 replies
bel.jad5
Sep 18, 2016
sqing
an hour ago
J
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An inequality
JK1603JK   2
N an hour ago by JK1603JK
Source: unknown
Let a,b,c>=0: ab+bc+ca=3 then maximize P=\frac{a^2b+b^2c+c^2a+9}{a+b+c}+\frac{abc}{2}.
2 replies
JK1603JK
6 hours ago
JK1603JK
an hour ago
J
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Time to bring it on!
giangtruong13   0
2 hours ago
Source: New probs
Prove that the equation $$x^2+y^2-z^2+2=xyz$$has no integer solutions
0 replies
giangtruong13
2 hours ago
0 replies
J
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JBMO Shortlist 2020 N4
Lukaluce   5
N 2 hours 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
2 hours ago
J
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Inspired by JK1603JK
sqing   1
N 2 hours 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
2 hours ago
sqing
2 hours ago
J
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Abelkonkurransen 2025 3a
Lil_flip38   4
N 2 hours 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
Lil_flip38
5 hours ago
Lil_flip38
2 hours ago
J
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postaffteff
JetFire008   15
N 2 hours 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
2 hours ago
J
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MTRP Subjective P2.2(Seniors)
sanyalarnab   1
N 2 hours 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
2 hours ago
J
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(x-2y)/y + (2y-4)/x + 4/xy = 0 and 1/x + 1/y+ 1/z =2
parmenides51   2
N 2 hours 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
2 hours ago
J
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J
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Loop of Logarithms
scls140511   11
N Yesterday at 10:36 PM by ohiorizzler1434
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 $\log_3 \log_2 m$.
11 replies
scls140511
Sep 8, 2024
ohiorizzler1434
Yesterday at 10:36 PM
J
Loop of Logarithms
G H J
Reveal topic tags
logarithms
L
G H BBookmark kLocked kLocked NReply
Source: 2024 China Round 1 (Gao Lian)
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scls140511
106 posts
scls140511
#1 h  Sep 8, 2024, 12:48 PM
Y by
Round 1

1 Real number $m>1$ satisfies $\log_9 \log_8 m =2024$. Find the value of $\log_3 \log_2 m$.
This post has been edited 4 times. Last edited by scls140511, Sep 8, 2024, 2:23 PM
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Aaronjudgeisgoat
826 posts
Aaronjudgeisgoat
#2 h  Sep 8, 2024, 1:05 PM • 4 Y
Y by MihaiT, entropybagel, aidan0626, sami1618
Click to reveal hidden text

kinda iffy but heres my sol
This post has been edited 1 time. Last edited by Aaronjudgeisgoat, Sep 8, 2024, 1:05 PM
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student1212
18 posts
student1212
#3 h  Sep 20, 2024, 5:33 AM
Y by
now from the question lets start taking log function i . e , $\log_3 \log_2 m$
after solving we would get 4049 as ans
This post has been edited 1 time. Last edited by student1212, Sep 20, 2024, 5:34 AM
Reason: .
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AshAuktober
927 posts
AshAuktober
#4 h  Sep 20, 2024, 4:02 PM • 2 Y
Y by WuQingjia, sami1618
Note that $m = 8^{9^{2024}}$, so $$\log_2{m} = 3\cdot9^{2024} = 3^{2 \cdot 2024 + 1}$$$$\implies \log_3{\log_2{m}} = \log_3{3^{2 \cdot 2024 + 1}} = \boxed{4049}.$$
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AMM11374
2 posts
AMM11374
#5 h  Oct 16, 2024, 8:16 AM
Y by
that seems so silly
Z K Y
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Neeka_s08
7 posts
Neeka_s08
#8 h  Dec 21, 2024, 4:29 PM • 5 Y
Y by sami1618, HEGZAM_BANDS, Ba_2008, Zhinaaf08, Ida_m
This my solution
Attachments:
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Topiary
22 posts
Topiary
#10 h  Tuesday at 9:56 PM
Y by
The equation is equivalent to $\log_8 m = 9^{2024} \equiv \log_8 3^{4049}\rightarrow m = 8^{3^{4048}} \rightarrow m = 2^{3^4049} \rightarrow \log_3 \log_2 m = \boxed{4049}$
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ohiorizzler1434
716 posts
ohiorizzler1434
#11 h  Tuesday at 10:14 PM
Y by
Bruh! How is this even from the China TSTs? This is too trivial.
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epl1
119 posts
epl1
#12 h  Tuesday at 10:16 PM
Y by
sol
Also, what kind of competition was this problem from?
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mpcnotnpc
28 posts
mpcnotnpc
#13 h  Yesterday at 2:59 PM
Y by
ohiorizzler1434 wrote:
Bruh! How is this even from the China TSTs? This is too trivial.

Gao lian is the very first part of the test, which means its equivalent to America's AMCs.
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SomeonecoolLovesMaths
3142 posts
SomeonecoolLovesMaths
#14 h  Yesterday at 3:12 PM
Y by
Storage
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ohiorizzler1434
716 posts
ohiorizzler1434
#15 h  Yesterday at 10:36 PM
Y by
mpcnotnpc wrote:
ohiorizzler1434 wrote:
Bruh! How is this even from the China TSTs? This is too trivial.

Gao lian is the very first part of the test, which means its equivalent to America's AMCs.

Ohhhh! Thanks for clarifying!
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