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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 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]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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[PMO27 Qualis] III. 1 Binary Counting
tapilyoca   5
N 7 minutes ago by Magdalo
John wrote down all of the numbers from 1 to 128 in binary. How many 1's did he write?
5 replies
tapilyoca
Nov 23, 2024
Magdalo
7 minutes ago
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22nd PMO Qualifying Stage #11
pensive   3
N 20 minutes ago by Magdalo
Let $x$ and $y$ be positive real numbers such that
\[ \log_x 64 + \log_{y^2} 16 = \frac{5}{3} \quad \text{and} \quad \log_y 64 + \log_{x^2} 16 = 1 \]What is the value of $\log_2 (xy)$?

Answer
3 replies
pensive
2 hours ago
Magdalo
20 minutes ago
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[PMO22 Qualifying] I.11
Magdalo   3
N 21 minutes ago by Magdalo
Let $x$ and $y$ be positive real numbers such that
\[\log_x64+\log_{y^2}16=\dfrac{5}{3}\text{ and }\log_y64+\log_{x^2}16=1 \]Find $\log_2(xy)$
3 replies
Magdalo
an hour ago
Magdalo
21 minutes ago
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Log Rationality
Magdalo   1
N 21 minutes ago by Magdalo
Let $x+y=36$ be positive integers. How many pairs of $x,y$ are there such that $\log_xy$ is rational?
1 reply
Magdalo
23 minutes ago
Magdalo
21 minutes ago
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diophantine equation
m4thbl3nd3r   1
N an hour ago by whwlqkd
Find all positive integers $n,k$ such that $$5^{2n+1}-5^n+1=k^2$$
1 reply
m4thbl3nd3r
Today at 10:34 AM
whwlqkd
an hour ago
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ISI UGB 2025 P2
SomeonecoolLovesMaths   11
N an hour ago by ProMaskedVictor
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.
11 replies
SomeonecoolLovesMaths
May 11, 2025
ProMaskedVictor
an hour ago
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Functional Inequaility
ariopro1387   2
N an hour ago by Triborg-V
Source: Own
Find all functions \(f: \mathbb{R} \rightarrow \mathbb{R}\) such that for any real numbers \(x\) and \(y\), the following inequality holds:
\[ f\left(x^2+2y f(x)\right) + (f(y))^2 \leq (f(x+y))^2 \]
2 replies
ariopro1387
Apr 9, 2025
Triborg-V
an hour ago
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Problem 7
SlovEcience   4
N an hour ago by SlovEcience
Consider the sequence \((u_n)\) defined by \(u_0 = 5\) and
\[ u_{n+1} = \frac{1}{2}u_n^2 - 4 \quad \text{for all } n \in \mathbb{N}. \]a) Prove that there exist infinitely many positive integers \(n\) such that \(u_n > 2020n\).

b) Compute
\[ \lim_{n \to \infty} \frac{2u_{n+1}}{u_0u_1\cdots u_n}. \]
4 replies
+1 w
SlovEcience
May 14, 2025
SlovEcience
an hour ago
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Orthocentres of triangles ABC and AB’C’
Stun   40
N an hour ago by mathwiz_1207
Source: IMO Shortlist 1995, G8
Suppose that $ ABCD$ is a cyclic quadrilateral. Let $ E = AC\cap BD$ and $ F = AB\cap CD$. Denote by $ H_{1}$ and $ H_{2}$ the orthocenters of triangles $ EAD$ and $ EBC$, respectively. Prove that the points $ F$, $ H_{1}$, $ H_{2}$ are collinear.

Original formulation:

Let $ ABC$ be a triangle. A circle passing through $ B$ and $ C$ intersects the sides $ AB$ and $ AC$ again at $ C'$ and $ B',$ respectively. Prove that $ BB'$, $CC'$ and $ HH'$ are concurrent, where $ H$ and $ H'$ are the orthocentres of triangles $ ABC$ and $ AB'C'$ respectively.
40 replies
Stun
Mar 13, 2005
mathwiz_1207
an hour ago
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JBMO TST Bosnia and Herzegovina 2023 P3
FishkoBiH   1
N an hour ago by Maths_VC
Source: JBMO TST Bosnia and Herzegovina 2023 P3
Let ABC be an acute triangle with an incenter $I$.The Incircle touches sides $AC$ and $AB$ in $E$ and $F$ ,respectively. Lines CI and EF intersect at $S$. The point $T$≠$I$ is on the line AI so that $EI$=$ET$.If $K$ is the foot of the altitude from $C$ in triangle $ABC$,prove that points $K$,$S$ and $T$ are colinear.
1 reply
FishkoBiH
3 hours ago
Maths_VC
an hour ago
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number theory diophantic with factorials and primes
skellyrah   5
N 2 hours ago by GreekIdiot
Source: by me
find all triplets of non negative integers (a,b,p) where p is prime such that $$ a! + b! + 7ab = p^2 $$
5 replies
skellyrah
Feb 16, 2025
GreekIdiot
2 hours ago
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Rational coefficients polynomial
Cats_on_a_computer   0
2 hours ago
Given a quartic monic polynomial with rational coefficients, show that if the polynomial has exactly 1 real root r, r must be rational.
I solved this somewhat differently (using the division algorithm), but it really seems like Vieta should work here. I haven’t been able to find another workable solution however.
0 replies
Cats_on_a_computer
2 hours ago
0 replies
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JBMO TST Bosnia and Herzegovina 2024 P2
FishkoBiH   1
N 2 hours ago by Rotten_
Source: JBMO TST Bosnia and Herzegovina 2024 P2
Determine all $x$, $y$, $k$ and $n$ positive integers such that:

$10^x$ + $10^y$ + $n!$ = $2024^k$

1 reply
FishkoBiH
3 hours ago
Rotten_
2 hours ago
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JBMO TST Bosnia and Herzegovina 2024 P1
FishkoBiH   2
N 2 hours ago by grupyorum
Source: JBMO TST Bosnia and Herzegovina 2024 P1
Let $a$,$b$,$c$ be real numbers different from 0 for which $ab$ + $bc$+ $ca$ = 0 holds
a) Prove that ($a$+$b$)($b$+$c$)($c$+$a$)≠ 0
b) Let $X$ = $a$ + $b$ + $c$ and $Y$ = $\frac{1}{a+b}$ + $\frac{1}{b+c}$ + $\frac{1}{c+a}$. Prove that numbers $X$ and $Y$ are both positive or both negative.
2 replies
FishkoBiH
3 hours ago
grupyorum
2 hours ago
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[CMC ARML 2020 I3] Unique Sequence
franchester   2
N Apr 28, 2025 by CubeAlgo15
There is a unique nondecreasing sequence of positive integers $a_1$, $a_2$, $\ldots$, $a_n$ such that \[\left(a_1+\frac1{a_1}\right)\left(a_2+\frac1{a_2}\right)\cdots\left(a_n+\frac1{a_n}\right)=2020.\]Compute $a_1+a_2+\cdots+a_n$.

Proposed by lminsl
2 replies
franchester
May 29, 2020
CubeAlgo15
Apr 28, 2025
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[CMC ARML 2020 I3] Unique Sequence
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franchester
1487 posts
franchester
#1 h  May 29, 2020, 11:52 PM
Y by
There is a unique nondecreasing sequence of positive integers $a_1$, $a_2$, $\ldots$, $a_n$ such that \[\left(a_1+\frac1{a_1}\right)\left(a_2+\frac1{a_2}\right)\cdots\left(a_n+\frac1{a_n}\right)=2020.\]Compute $a_1+a_2+\cdots+a_n$.

Proposed by lminsl
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thinkmath_
67 posts
thinkmath_
#2 h  May 30, 2020, 2:17 AM
Y by
amazing problem; just realize they all have to be like 1, 2, 10 or smth along those lines
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CubeAlgo15
43 posts
CubeAlgo15
#3 h  Apr 28, 2025, 6:09 PM
Y by
the sequence is 1 1 1 1 1 2 2 10
which gives the answer of 19 (not sure if this is correct but should be)
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