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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 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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VOLUNTEERING OPPORTUNITIES OPEN TO HIGH/MIDDLE SCHOOLERS
im_space_cadet   3
N 7 minutes ago by fossasor
Hi everyone!
Do you specialize in contest math? Do you have a passion for teaching? Do you want to help leverage those college apps? Well, I have something for all of you.

I am im_space_cadet, and during the fall of last year, I opened my non-profit DeltaMathPrep which teaches students preparing for contest math the problem-solving skills they need in order to succeed at these competitions. Currently, we are very much understaffed and would greatly appreciate the help of more tutors on our platform.

Each week on Saturday and Wednesday, we meet once for each competition: Wednesday for AMC 8 and Saturday for AMC 10 and we go over a past year paper for the entire class. On both of these days, we meet at 9PM EST in the night.

This is a great opportunity for anyone who is looking to have a solid activity to add to their college resumes that requires low effort from tutors and is very flexible with regards to time.

This is the link to our non-profit for anyone who would like to view our initiative:
https://www.deltamathprep.org/

If you are interested in this opportunity, please send me a DM on AoPS or respond to this post expressing your interest. I look forward to having you all on the team!

Thanks,
im_space_cadet
3 replies
im_space_cadet
an hour ago
fossasor
7 minutes ago
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Some problems
hashbrown2009   3
N 12 minutes ago by giangtruong13
1. Real numbers a,b,c are satisfy a+1/b = b+1/c = c+1/a =x. If a,b,c are distinct, what is the value of x?
2. If x^2+y^2=1, then what is the value of : root(x^2-2x+1) + root(xy-2x+y-2) ?
3. Find the value of the sequence 2^2 + (3^2+1) + (4^2+2) + … + (97^2+95) + (98^2+96).
4. If x^2+x-1=0, then evaluate (1-x^2-x^3-x^4-…-x^2022-x^2023)/x^2022 .
5. If triangle XYZ has 3 sides that are all whole numbers, and the perimeter of XYZ is 24, what is the probability XYZ is a right triangle?

Note: If someone can latex-ify this it would help.
3 replies
1 viewing
hashbrown2009
Yesterday at 11:01 PM
giangtruong13
12 minutes ago
J
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Graph of polynomials
Ecrin_eren   0
15 minutes ago
Sure! Here's the same translation without LaTeX:


---

The graph of the quadratic polynomial with real coefficients y = px^2 + qx + r, called G1, intersects the graph of the polynomial y = x^2, called G2, at points A and B. The lines tangent to G2 at points A and B intersect at point C. It is known that point C lies on G1. What is the value of p?

0 replies
Ecrin_eren
15 minutes ago
0 replies
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Find the value
sqing   9
N 19 minutes ago by sqing
Source: 2025 Tsinghua University
Let $A= \lim_{n\to\infty}\tan^n\left(\frac{\pi}{4}+\frac{1}{n}\right) . $ Find the value of $[100A] .$
9 replies
sqing
5 hours ago
sqing
19 minutes ago
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Dear Sqing: So Many Inequalities...
hashtagmath   30
N 26 minutes ago by sqing
I have noticed thousands upon thousands of inequalities that you have posted to HSO and was wondering where you get the inspiration, imagination, and even the validation that such inequalities are true? Also, what do you find particularly appealing and important about specifically inequalities rather than other branches of mathematics? Thank you :)
30 replies
hashtagmath
Oct 30, 2024
sqing
26 minutes ago
J
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Advanced topics in Inequalities
va2010   14
N 38 minutes ago by sqing
So a while ago, I compiled some tricks on inequalities. You are welcome to post solutions below!
14 replies
1 viewing
va2010
Mar 7, 2015
sqing
38 minutes ago
J
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The point F lies on the line OI in triangle ABC
WakeUp   13
N 42 minutes ago by Nari_Tom
Source: All-Russian Olympiad 2012 Grade 10 Day 2
The point $E$ is the midpoint of the segment connecting the orthocentre of the scalene triangle $ABC$ and the point $A$. The incircle of triangle $ABC$ incircle is tangent to $AB$ and $AC$ at points $C'$ and $B'$ respectively. Prove that point $F$, the point symmetric to point $E$ with respect to line $B'C'$, lies on the line that passes through both the circumcentre and the incentre of triangle $ABC$.
13 replies
WakeUp
May 31, 2012
Nari_Tom
42 minutes ago
J
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Very Easy Combinatorics Problem
zeta1   3
N an hour ago by franklin2013
Ali and Veli goes to hunting. The probability that each will successfully hit a duck is $1/2$ on any given shot. During the hunt, Ali shoots $12$ times, and Veli shoots $13$ times. What is the probability that Veli hits more ducks than Ali?

$ \textbf{(A)}\ \dfrac 12 \qquad\textbf{(B)}\ \dfrac{13}{25} \qquad\textbf{(C)}\ \dfrac{13}{24} \qquad\textbf{(D)}\ \dfrac{7}{13} \qquad\textbf{(E)}\ \dfrac{3}{4} $
3 replies
+1 w
zeta1
Today at 8:51 AM
franklin2013
an hour ago
J
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VOLUNTEERING OPPORTUNITY OPEN TO HIGH/MIDDLE SCHOOLERS
im_space_cadet   0
an hour ago
Hi everyone!
Do you specialize in contest math? Do you have a passion for teaching? Do you want to help leverage those college apps? Well, I have something for all of you.

I am im_space_cadet, and during the fall of last year, I opened my non-profit DeltaMathPrep which teaches students preparing for contest math the problem-solving skills they need in order to succeed at these competitions. Currently, we are very much understaffed and would greatly appreciate the help of more tutors on our platform.

Each week on Saturday and Wednesday, we meet once for each competition: Wednesday for AMC 8 and Saturday for AMC 10 and we go over a past year paper for the entire class. On both of these days, we meet at 9PM EST in the night.

This is a great opportunity for anyone who is looking to have a solid activity to add to their college resumes that requires low effort from tutors and is very flexible with regards to time.

This is the link to our non-profit for anyone who would like to view our initiative:
https://www.deltamathprep.org/

If you are interested in this opportunity, please send me a DM on AoPS or respond to this post expressing your interest. I look forward to having you all on the team!

Thanks,
im_space_cadet
0 replies
im_space_cadet
an hour ago
0 replies
J
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(2^n -1)!! -1 is divided by 2^n
parmenides51   5
N an hour ago by parmenides51
Source: 2023 Grand Duchy of Lithuania, MC p4 (Baltic Way TST)
Note that $k\ge 1$ for an odd natural number $$k! ! = k \cdot (k - 2) \cdot ... \cdot 1.$$Prove that $2^n$ divides $(2^n -1)!! -1$ for all $n \ge 3$.
5 replies
parmenides51
Mar 23, 2024
parmenides51
an hour ago
J
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Transforming a grid to another
Severus   3
N an hour ago by Project_Donkey_into_M4
Source: STEMS 2021 Cat B P5
Sheldon was really annoying Leonard. So to keep him quiet, Leonard decided to do something. He gave Sheldon the following grid

$\begin{tabular}{|c|c|c|c|c|c|} \hline 1 & 1 & 1 & 1 & 1 & 0\\ \hline 1 & 1 & 1 & 1 & 0 & 0\\ \hline 1 & 1 & 1 & 0 & 0 & 0\\ \hline 1 & 1 & 0 & 0 & 0 & 1\\ \hline 1 & 0 & 0 & 0 & 1 & 0\\ \hline 0 & 0 & 0 & 1 & 0 & 0\\ \hline \end{tabular}$

and asked him to transform it to the new grid below

$\begin{tabular}{|c|c|c|c|c|c|} \hline 1 & 2 & 18 &24 &28 &30\\ \hline 21 & 3 & 4 &16 &22 &26\\ \hline 23 &19 & 5 & 6 &14 &20\\ \hline 32 &25 &17 & 7 & 8 &12\\ \hline 33 &34 &27 &15 & 9 &10\\ \hline 35 &31 &36 &29 &13 &11\\ \hline \end{tabular}$

by only applying the following algorithm:

$\bullet$ At each step, Sheldon must choose either two rows or two columns.

$\bullet$ For two columns $c_1, c_2$, if $a,b$ are entries in $c_1, c_2$ respectively, then we say that $a$ and $b$ are corresponding if they belong to the same row. Similarly we define corresponding entries of two rows. So for Sheldon's choice, if two corresponding entries have the same parity, he should do nothing to them, but if they have different parities, he should add 1 to both of them.

Leonard hoped this would keep Sheldon occupied for some time, but Sheldon immediately said, "But this is impossible!". Was Sheldon right? Justify.
3 replies
1 viewing
Severus
Jan 24, 2021
Project_Donkey_into_M4
an hour ago
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Inspired by Bet667
sqing   1
N an hour ago by sqing
Source: Own
Let $ x,y\ge 0 $ such that $k(x+y)=1+xy. $ Prove that$$x+k^2y+\frac{1}{x}+\frac{k^2}{y} \geq \frac{k^2(k+1)^2+(k-1)^2}{k}$$Where $ k\in N^+.$
Let $ x,y\ge 0 $ such that $2(x+y)=1+xy. $ Prove that$$x+4y+\frac{1}{x}+\frac{4}{y} \geq \frac{37}{2}$$
1 reply
sqing
Today at 3:10 AM
sqing
an hour ago
J
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FE inequality from Iran
mojyla222   2
N an hour ago by sami1618
Source: Iran 2025 second round P5
Find all functions $f:\mathbb{R}^+ \to \mathbb{R}$ such that for all $x,y,z>0$
$$ 3(x^3+y^3+z^3)\geq f(x+y+z)\cdot f(xy+yz+xz) \geq (x+y+z)(xy+yz+xz). $$
2 replies
mojyla222
Yesterday at 9:20 AM
sami1618
an hour ago
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Not homogenous inequality
Nguyenhuyen_AG   0
an hour ago
Let $a,b,c$ are positive real numbers. Prove that
\[\frac{1}{(2a+1)(2b+1)}+\frac{1}{(2b+1)(2c+1)}+\frac{1}{(2c+1)(2a+1)} \geqslant \frac{3}{3+2(ab+bc+ca)}.\]
0 replies
Nguyenhuyen_AG
an hour ago
0 replies
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A Nice Problem
ilikemath247365   4
N Apr 14, 2025 by jkim0656
Find all real triples $(a, b, c)$ such that

$(2^{2a} + 1)(2^{2b} + 2)(2^{2c} + 8) = 2^{a + b + c + 5}$.
4 replies
ilikemath247365
Apr 14, 2025
jkim0656
Apr 14, 2025
J
A Nice Problem
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Reveal topic tags
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ilikemath247365
243 posts
ilikemath247365
#1 h  Apr 14, 2025, 4:47 PM
Y by
Find all real triples $(a, b, c)$ such that

$(2^{2a} + 1)(2^{2b} + 2)(2^{2c} + 8) = 2^{a + b + c + 5}$.
Z K Y
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alexheinis
10548 posts
alexheinis
#2 h  Apr 14, 2025, 5:00 PM
Y by
We can write $(2^a+{1\over {2^a}})(2^b+{2\over {2^b}})(2^c+{8\over{2^c}})=32$.
Now $2^a+{1\over {2^a}}=p+{1\over p}\ge 2, q+{2\over q}\ge 2\sqrt{2}$ and $r+{8\over r}\ge 4\sqrt{2}$.
Hence LHS$\ge 32$ and we have equality everywhere. Then $a=0,b=1/2,c=3/2$.
Z K Y
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programjames1
3045 posts
programjames1
#3 h  Apr 14, 2025, 5:00 PM
Y by
Solution
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ilikemath247365
243 posts
ilikemath247365
#4 h  Apr 14, 2025, 5:01 PM
Y by
My solution:

Click to reveal hidden text
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jkim0656
858 posts
jkim0656
#5 h  Apr 14, 2025, 5:06 PM
Y by
this is a very nice problem
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