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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.

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[*]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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ISI UGB 2025 P5
SomeonecoolLovesMaths   1
N 23 minutes ago by Primeniyazidayi
Source: ISI UGB 2025 P5
Let $a,b,c$ be nonzero real numbers such that $a+b+c \neq 0$. Assume that $$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a+b+c}$$Show that for any odd integer $k$, $$\frac{1}{a^k} + \frac{1}{b^k} + \frac{1}{c^k} = \frac{1}{a^k+b^k+c^k}.$$
1 reply
SomeonecoolLovesMaths
39 minutes ago
Primeniyazidayi
23 minutes ago
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ISI UGB 2025 P7
SomeonecoolLovesMaths   0
25 minutes ago
Source: ISI UGB 2025 P7
Consider a ball that moves inside an acute-angled triangle along a straight line, unit it hits the boundary, which is when it changes direction according to the mirror law, just like a ray of light (angle of incidence = angle of reflection). Prove that there exists a triangular periodic path for the ball, as pictured below.

IMAGE
0 replies
SomeonecoolLovesMaths
25 minutes ago
0 replies
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ISI UGB 2025 P4
SomeonecoolLovesMaths   0
29 minutes ago
Source: ISI UGB 2025 P4
Let $S^1 = \{ z \in \mathbb{C} \mid |z| =1 \}$ be the unit circle in the complex plane. Let $f \colon S^1 \longrightarrow S^2$ be the map given by $f(z) = z^2$. We define $f^{(1)} \colon = f$ and $f^{(k+1)} \colon = f \circ f^{(k)}$ for $k \geq 1$. The smallest positive integer $n$ such that $f^{(n)}(z) = z$ is called the period of $z$. Determine the total number of points in $S^1$ of period $2025$.
(Hint : $2025 = 3^4 \times 5^2$)
0 replies
SomeonecoolLovesMaths
29 minutes ago
0 replies
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ISI UGB 2025 P8
SomeonecoolLovesMaths   0
33 minutes ago
Source: ISI UGB 2025 P8
Let $n \geq 2$ and let $a_1 \leq a_2 \leq \cdots \leq a_n$ be positive integers such that $\sum_{i=1}^{n} a_i = \prod_{i=1}^{n} a_i$. Prove that $\sum_{i=1}^{n} a_i \leq 2n$ and determine when equality holds.
0 replies
SomeonecoolLovesMaths
33 minutes ago
0 replies
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ISI UGB 2025 P6
SomeonecoolLovesMaths   0
35 minutes ago
Source: ISI UGB 2025 P6
Let $\mathbb{N}$ denote the set of natural numbers, and let $\left( a_i, b_i \right)$, $1 \leq i \leq 9$, be nine distinct tuples in $\mathbb{N} \times \mathbb{N}$. Show that there are three distinct elements in the set $\{ 2^{a_i} 3^{b_i} \colon 1 \leq i \leq 9 \}$ whose product is a perfect cube.
0 replies
SomeonecoolLovesMaths
35 minutes ago
0 replies
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ISI UGB 2025 P2
SomeonecoolLovesMaths   0
37 minutes ago
Source: ISI UGB 2025 P2
If the interior angles of a triangle $ABC$ satisfy the equality, $$\sin ^2 A + \sin ^2 B + \sin^2 + C = 2 \left( \cos ^2 A + \cos ^2 B + \cos ^2 C \right),$$prove that the triangle must have a right angle.
0 replies
SomeonecoolLovesMaths
37 minutes ago
0 replies
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Six variables
Nguyenhuyen_AG   1
N an hour ago by TNKT
Let $a,\,b,\,c,\,x,\,y,\,z$ be six positive real numbers. Prove that
$$\frac{a}{b+c} \cdot \frac{y+z}{x} + \frac{b}{c+a} \cdot \frac{z+x}{y} + \frac{c}{a+b} \cdot \frac{x+y}{z} \geqslant 2+\sqrt{\frac{8abc}{(a+b)(b+c)(c+a)}}.$$
1 reply
+1 w
Nguyenhuyen_AG
Today at 5:09 AM
TNKT
an hour ago
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Anything real in this system must be integer
Assassino9931   3
N an hour ago by Sardor_lil
Source: Al-Khwarizmi International Junior Olympiad 2025 P1
Determine the largest integer $c$ for which the following statement holds: there exists at least one triple $(x,y,z)$ of integers such that
\begin{align*} x^2 + 4(y + z) = y^2 + 4(z + x) = z^2 + 4(x + y) = c \end{align*}and all triples $(x,y,z)$ of real numbers, satisfying the equations, are such that $x,y,z$ are integers.

Marek Maruin, Slovakia
3 replies
Assassino9931
May 9, 2025
Sardor_lil
an hour ago
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Interesting inequalities
sqing   3
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0 , (a+k )(b+c)=k+1.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2k-3+2\sqrt{k+1}}{3k-1}$$Where $ k\geq \frac{2}{3}.$
Let $ a,b,c\geq 0 , (a+1)(b+c)=2.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq 2\sqrt{2}-1$$Let $ a,b,c\geq 0 , (a+3)(b+c)=4.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{7}{4}$$Let $ a,b,c\geq 0 , (3a+2)(b+c)= 5.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2(2\sqrt{15}-5)}{3}$$
3 replies
sqing
Yesterday at 1:29 PM
sqing
an hour ago
J
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Interesting inequalities
sqing   1
N an hour ago by sqing
Source: Own
Let $ a,b>0 $ and $ a+b\leq 1 $ . Prove that
$$\left(\frac{1}{a^3}-1\right)\left(\frac{1}{b^3}-1\right)-k\left(\frac{a}{b}+\frac{b}{a}\right) \geq 49-2k$$Where $24\geq k\in N^+.$
$$\left(\frac{1}{a^3}-1\right)\left(\frac{1}{b^3}-1\right) \geq 49$$$$\left(\frac{1}{a^3}-1\right)\left(\frac{1}{b^3}-1\right)-25\left(\frac{a}{b}+\frac{b}{a}\right) \geq -\frac{13}{12}$$$$\left(\frac{1}{a^3}-1\right)\left(\frac{1}{b^3}-1\right)-26\left(\frac{a}{b}+\frac{b}{a}\right) \geq -\frac{10}{3}$$$$\left(\frac{1}{a^3}-1\right)\left(\frac{1}{b^3}-1\right)-27\left(\frac{a}{b}+\frac{b}{a}\right) \geq -\frac{23}{4}$$
1 reply
sqing
an hour ago
sqing
an hour ago
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Goals for 2025-2026
Airbus320-214   2
N 2 hours ago by AshAuktober
Please write down your goal/goals for competitions here for 2025-2026.
2 replies
Airbus320-214
4 hours ago
AshAuktober
2 hours ago
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MOP Emails Out! (not clickbait)
Mathandski   104
N 2 hours ago by ohiorizzler1434
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
104 replies
Mathandski
Apr 22, 2025
ohiorizzler1434
2 hours ago
J
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Past USAMO Medals
sdpandit   2
N 5 hours ago by sdpandit
Does anyone know where to find lists of USAMO medalists from past years? I can find the 2025 list on their website, but they don't seem to keep lists from previous years and I can't find it anywhere else. Thanks!
2 replies
sdpandit
May 8, 2025
sdpandit
5 hours ago
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Geo is back??
GoodMorning   137
N 6 hours ago by Siddharthmaybe
Source: 2023 USAJMO Problem 2/USAMO Problem 1
In an acute triangle $ABC$, let $M$ be the midpoint of $\overline{BC}$. Let $P$ be the foot of the perpendicular from $C$ to $AM$. Suppose that the circumcircle of triangle $ABP$ intersects line $BC$ at two distinct points $B$ and $Q$. Let $N$ be the midpoint of $\overline{AQ}$. Prove that $NB=NC$.

Proposed by Holden Mui
137 replies
GoodMorning
Mar 23, 2023
Siddharthmaybe
6 hours ago
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ros application results?
cowstalker   12
N Apr 17, 2025 by math_on_top
I recently applied to ROSS and just wondering when they come out, and if they come out to everyone at the same time? I want to know what date to look forward to because of other plans that depend on whether I get in or not.

12 replies
cowstalker
Apr 15, 2025
math_on_top
Apr 17, 2025
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ros application results?
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Reveal topic tags
Ross Mathematics Program
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cowstalker
295 posts
cowstalker
#1 h  Apr 15, 2025, 12:14 AM
Y by
I recently applied to ROSS and just wondering when they come out, and if they come out to everyone at the same time? I want to know what date to look forward to because of other plans that depend on whether I get in or not.
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miguel00
593 posts
miguel00
#2 h  Apr 15, 2025, 12:25 AM
Y by
Last year, the decision came out April 19th which was a Friday. I don't know about this year, but the trend (heard it from other people) seems to be that it comes out Friday of this week which is April 18th.
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trous
2 posts
trous
#3 h  Apr 15, 2025, 7:26 PM
Y by
miguel00 wrote:
Last year, the decision came out April 19th which was a Friday. I don't know about this year, but the trend (heard it from other people) seems to be that it comes out Friday of this week which is April 18th.
in 2023 decisions were sent out on thursday april 20....
This post has been edited 1 time. Last edited by trous, Apr 15, 2025, 7:29 PM
Reason: english mistake oops
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PaixiaoLover
123 posts
PaixiaoLover
#4 h  Apr 16, 2025, 12:47 AM
Y by
hopefully by friday
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ericbowenli
14 posts
ericbowenli
#5 h  Apr 16, 2025, 11:17 PM
Y by
pls before sumac payment ddl, lol
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scls140511
115 posts
scls140511
#6 h  Apr 17, 2025, 12:52 AM
Y by
kisonecat said he expect in the "next couple of days"
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clematishydragean
2 posts
clematishydragean
#7 h  Apr 17, 2025, 1:21 AM
Y by
Who is kisonecat?
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aa1024
1882 posts
aa1024
#8 h  Apr 17, 2025, 1:27 AM
Y by
clematishydragean wrote:
Who is kisonecat?

Professor Jim Fowler, director of the Ross Program at Ohio
This post has been edited 1 time. Last edited by aa1024, Apr 17, 2025, 1:27 AM
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clematishydragean
2 posts
clematishydragean
#9 h  Apr 17, 2025, 1:32 AM
Y by
Oh i see. Thank you.
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math_on_top
24 posts
math_on_top
#10 h  Apr 17, 2025, 10:26 PM
Y by
Am i cooked if i forgot to do the part wher it says to verify that 21, 33, 49, and 77 is 4-hilbert prme :skull:
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Danielzh
492 posts
Danielzh
#11 h  Apr 17, 2025, 10:29 PM
Y by
math_on_top wrote:
Am i cooked if i forgot to do the part wher it says to verify that 21, 33, 49, and 77 is 4-hilbert prme :skull:

imo that's the least important part, so nah :D
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ericbowenli
14 posts
ericbowenli
#12 h  Apr 17, 2025, 10:59 PM
Y by
math_on_top wrote:
Am i cooked if i forgot to do the part wher it says to verify that 21, 33, 49, and 77 is 4-hilbert prme :skull:

bruh that's not even part of the problem. It's just something that help u understand the definition
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math_on_top
24 posts
math_on_top
#13 h  Apr 17, 2025, 11:41 PM
Y by
ok i think i also mde a false conjecture about hilbert primes...
This post has been edited 1 time. Last edited by math_on_top, Apr 17, 2025, 11:42 PM
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