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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.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
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[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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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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Range if \omega for No Inscribed Right Triangle y = \sin(\omega x)
ThisIsJoe   0
3 minutes ago
For a positive number \omega , determine the range of \omega for which the curve y = \sin(\omega x) has no inscribed right triangle.
Could someone help me figure out how to approach this?
0 replies
ThisIsJoe
3 minutes ago
0 replies
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Inspired by Bet667
sqing   3
N 37 minutes ago by sqing
Source: Own
Let $ a,b $ be a real numbers such that $a^2+kab+b^2\ge a^3+b^3.$Prove that$$a+b\leq k+2$$Where $ k\geq 0. $
3 replies
sqing
Tuesday at 2:46 PM
sqing
37 minutes ago
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F has at least n distinct values
nataliaonline75   0
an hour ago

Let $n$ be natural number and $S$ be the set of $n$ distinct natural numbers. Define function $f: S \times S \rightarrow N$ with $f(x,y)=\frac{xy}{(gcd(x,y))^2}$. Prove that $f$ have at least $n$ distinct values.
0 replies
nataliaonline75
an hour ago
0 replies
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Junior Balkan Mathematical Olympiad 2020- P4
Lukaluce   11
N an hour ago by MR.1
Source: JBMO 2020
Find all prime numbers $p$ and $q$ such that
$$1 + \frac{p^q - q^p}{p + q}$$is a prime number.

Proposed by Dorlir Ahmeti, Albania
11 replies
Lukaluce
Sep 11, 2020
MR.1
an hour ago
J
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Interesting question from Al-Khwarezmi olympiad 2024 P3, day1
Adventure1000   1
N an hour ago by pooh123
Find all $x, y, z \in \left (0, \frac{1}{2}\right )$ such that
$$ \begin{cases} (3 x^{2}+y^{2}) \sqrt{1-4 z^{2}} \geq z; \\ (3 y^{2}+z^{2}) \sqrt{1-4 x^{2}} \geq x; \\ (3 z^{2}+x^{2}) \sqrt{1-4 y^{2}} \geq y. \end{cases} $$Proposed by Ngo Van Trang, Vietnam
1 reply
Adventure1000
Yesterday at 4:10 PM
pooh123
an hour ago
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one nice!
MihaiT   3
N an hour ago by Pin123
Find positiv integer numbers $(a,b) $ s.t. $\frac{a}{b-2} $ and $\frac{3b-6}{a-3}$ be positiv integer numbers.
3 replies
MihaiT
Jan 14, 2025
Pin123
an hour ago
J
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Prove that lines parallel in triangle
jasperE3   5
N an hour ago by Thapakazi
Source: Mongolian MO 2007 Grade 11 P1
Let $M$ be the midpoint of the side $BC$ of triangle $ABC$. The bisector of the exterior angle of point $A$ intersects the side $BC$ in $D$. Let the circumcircle of triangle $ADM$ intersect the lines $AB$ and $AC$ in $E$ and $F$ respectively. If the midpoint of $EF$ is $N$, prove that $MN\parallel AD$.
5 replies
jasperE3
Apr 8, 2021
Thapakazi
an hour ago
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JBMO Shortlist 2020 N6
Lukaluce   4
N 2 hours ago by MR.1
Source: JBMO Shortlist 2020
Are there any positive integers $m$ and $n$ satisfying the equation

$m^3 = 9n^4 + 170n^2 + 289$ ?
4 replies
Lukaluce
Jul 4, 2021
MR.1
2 hours ago
J
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Nice concyclicity involving triangle, circle center, and midpoints
Kizaruno   0
2 hours ago
Let triangle ABC be inscribed in a circle with center O. A line d intersects sides AB and AC at points E and D, respectively. Let M, N, and P be the midpoints of segments BD, CE, and DE, respectively. Let Q be the foot of the perpendicular from O to line DE. Prove that the points M, N, P, and Q lie on a circle.

0 replies
Kizaruno
2 hours ago
0 replies
J
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Acute Angle Altitudes... say that ten times fast
Math-lover1   1
N 2 hours ago by pooh123
In acute triangle $ABC$, points $D$ and $E$ are the feet of the angle bisector and altitude from $A$, respectively. Suppose that $AC-AB=36$ and $DC-DB=24$. Compute $EC-EB$.
1 reply
Math-lover1
Yesterday at 11:30 PM
pooh123
2 hours ago
J
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non-perfect square is non-quadratic residue mod some p
SpecialBeing2017   3
N 2 hours ago by ilovemath0402
If $n$ is not a perfect square, then there exists an odd prime $p$ s.t. $n$ is a quadratic non-residue mod $p$.
3 replies
SpecialBeing2017
Apr 14, 2023
ilovemath0402
2 hours ago
J
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Circles tangent at orthocenter
Achillys   62
N 2 hours ago by Rayvhs
Source: APMO 2018 P1
Let $H$ be the orthocenter of the triangle $ABC$. Let $M$ and $N$ be the midpoints of the sides $AB$ and $AC$, respectively. Assume that $H$ lies inside the quadrilateral $BMNC$ and that the circumcircles of triangles $BMH$ and $CNH$ are tangent to each other. The line through $H$ parallel to $BC$ intersects the circumcircles of the triangles $BMH$ and $CNH$ in the points $K$ and $L$, respectively. Let $F$ be the intersection point of $MK$ and $NL$ and let $J$ be the incenter of triangle $MHN$. Prove that $F J = F A$.
62 replies
Achillys
Jun 24, 2018
Rayvhs
2 hours ago
J
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Unsymmetric FE
Lahmacuncu   1
N 2 hours ago by ja.
Source: Own
Find all functions $f:\mathbb{R} \rightarrow \mathbb{R}$ that satisfies $f(x^2+xy+y)+f(x^2y)+f(xy^2)=2f(xy)+f(x)+f(y)$ for all real $(x,y)$
1 reply
Lahmacuncu
3 hours ago
ja.
2 hours ago
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find angle
TBazar   3
N 2 hours ago by TBazar
Given $ABC$ triangle with $AC>BC$. We take $M$, $N$ point on AC, AB respectively such that $AM=BC$, $CM=BN$. $BM$, $AN$ lines intersect at point $K$. If $2\angle AKM=\angle ACB$, find $\angle ACB$
3 replies
TBazar
Today at 6:57 AM
TBazar
2 hours ago
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J
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that statement is true
pennypc123456789   3
N Apr 5, 2025 by sqing
we have $a^3+b^3 = 2$ and $3(a^4+b^4)+2a^4b^4 \le 8 $ , then we can deduce $a^2+b^2$ \le 2 $ ?
3 replies
pennypc123456789
Mar 23, 2025
sqing
Apr 5, 2025
J
that statement is true
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Reveal topic tags
inqualities
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pennypc123456789
38 posts
pennypc123456789
#1 h  Mar 23, 2025, 9:27 AM
Y by
we have $a^3+b^3 = 2$ and $3(a^4+b^4)+2a^4b^4 \le 8 $ , then we can deduce $a^2+b^2$ \le 2 $ ?
This post has been edited 1 time. Last edited by pennypc123456789, Mar 23, 2025, 10:10 AM
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no_room_for_error
333 posts
no_room_for_error
#2 h  Mar 23, 2025, 11:15 AM • 2 Y
Y by ehuseyinyigit, pennypc123456789
pennypc123456789 wrote:
we have $a^3+b^3 = 2$ and $3(a^4+b^4)+2a^4b^4 \le 8 $ , then we can deduce $a^2+b^2 \le 2 $ ?

Just $3(a^4+b^4)+2a^4b^4\leq 8$ is enough. It follows from Cauchy-Schwarz

$$25 \geq (2a^4+3)(2b^4+3)\geq (2a^2+2b^2+1)^2$$
Z K Y
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pennypc123456789
38 posts
pennypc123456789
#3 h  Mar 23, 2025, 2:44 PM
Y by
wow thanks
Z K Y
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sqing
42049 posts
sqing
#4 h  Apr 5, 2025, 12:32 PM
Y by
Let $ a,b \geq 0 $ and $ a^3 +b^3=2. $ Prove that
$$3(a^4+b^4)+2a^4b^4\leq 8$$
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