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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.

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0 replies
jlacosta
May 1, 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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Inequalities
sqing   0
a minute ago
Let $ a,b,c\geq 0 , (a+8)(b+c)=9.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{38}{23}$$Let $ a,b,c\geq 0 , (a+2)(b+c)=3.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2(2\sqrt{3}+1)}{5}$$
0 replies
2 viewing
sqing
a minute ago
0 replies
J
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Unknown triangle area
smartvong   1
N 42 minutes ago by smartvong
The diagram shows a convex quadrilateral $ABCD$. The points $E$ and $F$ divide $AB$ into three equal parts while the points $G$ and $H$ divide $CD$ into three equal parts. The line segments $AH$ and $ED$ intersect at $I$. The line segments $CF$ and $BG$ intersect at $J$. Given that the areas of the triangles $AID$, $EHI$ and $FJG$ are $154$, $112$, and $99$ respectively, find the area of the triangle $BJC$.

IMAGE
1 reply
smartvong
May 8, 2025
smartvong
42 minutes ago
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interesting functional
Pomegranat   2
N an hour ago by Pomegranat
Source: I don't know sorry
Find all functions \( f : \mathbb{R}^+ \to \mathbb{R}^+ \) such that for all positive real numbers \( x \) and \( y \), the following equation holds:
\[ \frac{x + f(y)}{x f(y)} = f\left( \frac{1}{y} + f\left( \frac{1}{x} \right) \right) \]
2 replies
Pomegranat
3 hours ago
Pomegranat
an hour ago
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Geometry
AlexCenteno2007   4
N an hour ago by Raul_S_Baz
Let ABC be an acute triangle and let D, E and F be the feet of the altitudes from A, B and C respectively. The straight line EF and the circumcircle of ABC intersect at P such that F is between E and P, the straight lines BP and DF intersect at Q. Show that if ED = EP then CQ and DP are parallel.
4 replies
AlexCenteno2007
Apr 28, 2025
Raul_S_Baz
an hour ago
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Function equation algebra
TUAN2k8   1
N an hour ago by TUAN2k8
Source: Balkan MO 2025
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x \in \mathbb{R}$ and $y \in \mathbb{R}$,
\begin{align} f(x+yf(x))+y=xy+f(x+y). \end{align}
1 reply
TUAN2k8
an hour ago
TUAN2k8
an hour ago
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Functional equation with a twist (it's number theory)
Davdav1232   1
N an hour ago by NO_SQUARES
Source: Israel TST 8 2025 p2
Prove that for all primes \( p \) such that \( p \equiv 3 \pmod{4} \) or \( p \equiv 5 \pmod{8} \), there exist integers
\[ 1 \leq a_1 < a_2 < \cdots < a_{(p-1)/2} < p \]such that
\[ \prod_{\substack{1 \leq i < j \leq (p-1)/2}} (a_i + a_j)^2 \equiv 1 \pmod{p}. \]
1 reply
Davdav1232
Thursday at 8:32 PM
NO_SQUARES
an hour ago
J
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Inequalities
sqing   1
N an hour ago by sqing
Let $ 0\leq x,y,z\leq 2. $ Prove that
$$-48\leq (x-yz)( 3y-zx)(z-xy)\leq 9$$$$-144\leq (3x-yz)(y-zx)(3z-xy)\leq\frac{81}{64}$$$$-144\leq (3x-yz)(2y-zx)(3z-xy)\leq\frac{81}{16}$$
1 reply
sqing
Yesterday at 8:50 AM
sqing
an hour ago
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Coolabra
Titibuuu   3
N an hour ago by sqing
Let \( a, b, c \) be distinct real numbers such that
\[ a + b + c + \frac{1}{abc} = \frac{19}{2} \]Find the maximum possible value of \( a \).
3 replies
Titibuuu
Today at 2:21 AM
sqing
an hour ago
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Is the result of this is the same as cauchy?
ItzsleepyXD   0
2 hours ago
Source: curiosity
Prove or disprove that for all continuous or monotonic function $f : \mathbb{R}^2 \to \mathbb{R}$ .The solution to $$f(a,x)+f(b,y)=f(a+b,x+y) \text{ for all }a,b,x,y \in \mathbb{R}$$is only $f(x,y)=cx+dy$ for some $c,d \in \mathbb{R}$
0 replies
ItzsleepyXD
2 hours ago
0 replies
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a fractions problem
kjhgyuio   1
N 2 hours ago by Ash_the_Bash07
.........
1 reply
kjhgyuio
2 hours ago
Ash_the_Bash07
2 hours ago
J
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Maximum area of a triangle
Kunihiko_Chikaya   1
N 2 hours ago by Mathzeus1024
Source: 2008 Keio University entrance exam/Medical
(1) For $ \alpha > - 5$, consider the two circles on $ xy$ plane: $ O_1: x^2 + y^2 = 1,\ O_2: x^2 + 2x + y^2 - 4y - \alpha = 0$. Find the range of $ \alpha$ for which these circles have two intersection points, then find the equation of the line passing through these points.

(2) Given points $ A,\ B,\ P$ on the perimeter of a circle with radius 1. Let the length of the cord $ AB = r\ (0 < r\leq 2)$. When two points move on the circle, find the maximum area of $ \triangle{ABP}$.
1 reply
Kunihiko_Chikaya
Feb 22, 2008
Mathzeus1024
2 hours ago
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algebraic inequality
produit   1
N 2 hours ago by sqing
Positive a, b, c satisfy a + b + c = ab + bc + ca. Prove that
a + b + c + 1 ⩾ 4abc.
1 reply
produit
2 hours ago
sqing
2 hours ago
J
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2001-th sequence term less than 1001
orl   6
N 2 hours ago by Bryan0224
Source: CWMO 2001, Problem 1
The sequence $ \{x_n\}$ satisfies $ x_1 = \frac {1}{2}, x_{n + 1} = x_n + \frac {x_n^2}{n^2}$. Prove that $ x_{2001} < 1001$.
6 replies
orl
Dec 27, 2008
Bryan0224
2 hours ago
J
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inequality involving GCD and square roots
gaussious   0
2 hours ago
how to even approach this?
0 replies
gaussious
2 hours ago
0 replies
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J
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Help me please
Hahahsafdk3l   2
N Mar 29, 2025 by Hahahsafdk3l
Find all functions $f: \mathbb{R^+} \to \mathbb{R^+}$ such that $f(2f(x) + f(y) + xyy) = xy + 2x + y, \forall x, y > 0$
2 replies
Hahahsafdk3l
Mar 29, 2025
Hahahsafdk3l
Mar 29, 2025
J
Help me please
G H J
Reveal topic tags
functional equation
function
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Hahahsafdk3l
32 posts
Hahahsafdk3l
#1 h  Mar 29, 2025, 2:21 AM
Y by
Find all functions $f: \mathbb{R^+} \to \mathbb{R^+}$ such that $f(2f(x) + f(y) + xyy) = xy + 2x + y, \forall x, y > 0$
Z K Y
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jasperE3
11317 posts
jasperE3
#2 h  Mar 29, 2025, 2:40 AM
Y by
Hahahsafdk3l wrote:
Find all functions $f: \mathbb{R^+} \to \mathbb{R^+}$ such that $f(2f(x) + f(y) + xyy) = xy + 2x + y, \forall x, y > 0$

Almost certainly a typo of this question.
https://artofproblemsolving.com/community/c4h3536833p34392946
BTW there is a search function on AoPS that you can use, most problems you've posted have already been posted elsewhere on AoPS so there is no need for the post.
This post has been edited 2 times. Last edited by jasperE3, Mar 29, 2025, 2:53 AM
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Hahahsafdk3l
32 posts
Hahahsafdk3l
#3 h  Mar 29, 2025, 11:43 PM
Y by
thank you
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