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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

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0 replies
jlacosta
Mar 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
J
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Crazy number theory
MTA_2024   5
N 24 minutes ago by bjump
Find all couple $(p;q)$ of primes (greater than 5) such that : $$pq \mid (5^q-3^q)(5^p-3^p)$$
5 replies
MTA_2024
3 hours ago
bjump
24 minutes ago
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AMC 12 Question
sadas123   0
32 minutes ago
Hello! I am a 6th grader this year about to become 7th grade next year. I was wondering if I should take the AMC 12 next year because I think I am ready for it, I was thinking to do AMC 10 A and AMC 12 B, do you think it is a good idea? Here are the courses I finished and now I am working on:

Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1

Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon

Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???

Stats for AMC 12 (Mocked):

1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96

The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.
0 replies
sadas123
32 minutes ago
0 replies
J
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hard number theory problem
Zavyk09   0
33 minutes ago
Source: forgotten
Find all couple $(x, y)$ of positive integers such that:
$$2^n + 3^n \mid x^n + y^n, \forall n \in \mathbb{N}^*$$
0 replies
Zavyk09
33 minutes ago
0 replies
J
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The return of a legend inequality
giangtruong13   2
N 43 minutes ago by polishedhardwoodtable
Source: Legacy
Given that $0<a,b,c,d<1$.Prove that: $$ (1-a)(1-b)(1-c)(1-d) > 1-a-b-c-d $$
2 replies
giangtruong13
2 hours ago
polishedhardwoodtable
43 minutes ago
J
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Slightly weird points which are not so weird
Pranav1056   9
N an hour ago by Retemoeg
Source: India TST 2023 Day 4 P1
Suppose an acute scalene triangle $ABC$ has incentre $I$ and incircle touching $BC$ at $D$. Let $Z$ be the antipode of $A$ in the circumcircle of $ABC$. Point $L$ is chosen on the internal angle bisector of $\angle BZC$ such that $AL = LI$. Let $M$ be the midpoint of arc $BZC$, and let $V$ be the midpoint of $ID$. Prove that $\angle IML = \angle DVM$
9 replies
Pranav1056
Jul 9, 2023
Retemoeg
an hour ago
J
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2023 factors and perfect cube
proxima1681   4
N an hour ago by anudeep
Source: Indian Statistical Institute (ISI) UGB 2023 P4
Let $n_1, n_2, \cdots , n_{51}$ be distinct natural numbers each of which has exactly $2023$ positive integer factors. For instance, $2^{2022}$ has exactly $2023$ positive integer factors $1,2, 2^{2}, 2^{3}, \cdots 2^{2021}, 2^{2022}$. Assume that no prime larger than $11$ divides any of the $n_{i}$'s. Show that there must be some perfect cube among the $n_{i}$'s.
4 replies
proxima1681
May 14, 2023
anudeep
an hour ago
J
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circle geometry showing perpendicularity
Kyj9981   1
N an hour ago by Retemoeg
Two circles $\omega_1$ and $\omega_2$ intersect at points $A$ and $B$. A line through $B$ intersects $\omega_1$ and $\omega_2$ at points $C$ and $D$, respectively. Line $AD$ intersects $\omega_1$ at point $E \neq A$, and line $AC$ intersects $\omega_2$ at point $F \neq A$. If $O$ is the circumcenter of $\triangle AEF$, prove that $OB \perp CD$.
1 reply
Kyj9981
6 hours ago
Retemoeg
an hour ago
J
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Hard problem
Tendo_Jakarta   5
N an hour ago by Tendo_Jakarta
Let the sequence \(x_{n}\) be such that
\[u_{1} = 1; \quad u_{n+1} = \dfrac{u_{1} + u_{2} +...+u_{n}}{n}+n-1 \quad \forall n \in \mathbb{N^{*}}\]and \(y_{n} =\dfrac{1}{u_{1}u_{2}} + \dfrac{1}{u_{3}u_{4}} + ... + \dfrac{1}{u_{2n-1}u_{2n}} \quad \forall n \geq 1\). Find \(\lim_{n\rightarrow\infty}{y_{n}}\).
5 replies
Tendo_Jakarta
2 hours ago
Tendo_Jakarta
an hour ago
J
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Oh no! Inequality again?
mathisreaI   108
N an hour ago by Maximilian113
Source: IMO 2022 Problem 2
Let $\mathbb{R}^+$ denote the set of positive real numbers. Find all functions $f: \mathbb{R}^+ \to \mathbb{R}^+$ such that for each $x \in \mathbb{R}^+$, there is exactly one $y \in \mathbb{R}^+$ satisfying $$xf(y)+yf(x) \leq 2$$
108 replies
mathisreaI
Jul 13, 2022
Maximilian113
an hour ago
J
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Equation with powers
a_507_bc   5
N an hour ago by ali123456
Source: Serbia JBMO TST 2024 P1
Find all non-negative integers $x, y$ and primes $p$ such that $$3^x+p^2=7 \cdot 2^y.$$
5 replies
a_507_bc
May 25, 2024
ali123456
an hour ago
J
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hermoso, raiz primitiva, orden??
holaquehace707070   0
an hour ago
Sea n un numero natural con mas de 2021 dıgitos donde ninguno de el-
los es 8 o 9. Suponga que n no tiene factores comunes con 2021. Demuestre que es posible
aumentar uno de los dıgitos de n en a lo mas 2 de modo que el numero resultante sea multiplo
de 2021.
0 replies
holaquehace707070
an hour ago
0 replies
J
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AIME score for college apps
Happyllamaalways   85
N an hour ago by MC_ADe
What good colleges do I have a chance of getting into with an 11 on AIME? (Any chances for Princeton)

Also idk if this has weight but I had the highest AIME score in my school.
85 replies
Happyllamaalways
Mar 13, 2025
MC_ADe
an hour ago
J
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AMC 10.........
BAM10   11
N an hour ago by Andyluo
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
11 replies
BAM10
Mar 2, 2025
Andyluo
an hour ago
J
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rows are DERANGED and a SOCOURGE to usajmo .
GrantStar   27
N 2 hours ago by EGMO
Source: USAJMO 2024/4
Let $n \geq 3$ be an integer. Rowan and Colin play a game on an $n \times n$ grid of squares, where each square is colored either red or blue. Rowan is allowed to permute the rows of the grid and Colin is allowed to permute the columns. A grid coloring is orderly if: [list] [*]no matter how Rowan permutes the rows of the coloring, Colin can then permute the columns to restore the original grid coloring; and [*]no matter how Colin permutes the columns of the coloring, Rowan can then permute the rows to restore the original grid coloring. [/list] In terms of $n$, how many orderly colorings are there?

Proposed by Alec Sun
27 replies
GrantStar
Mar 21, 2024
EGMO
2 hours ago
J
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J
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AMC 10.........
BAM10   11
N an hour ago by Andyluo
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
11 replies
BAM10
Mar 2, 2025
Andyluo
an hour ago
J
AMC 10.........
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Reveal topic tags
AMC 10
AMC 8
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BAM10
67 posts
BAM10
#1 h  Mar 2, 2025, 8:02 PM
Y by
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
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orangebear
610 posts
orangebear
#2 h  Mar 2, 2025, 8:04 PM
Y by
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.
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CYW
326 posts
CYW
#3 h  Mar 2, 2025, 9:06 PM
Y by
Dunno, opposite way for me. I got 80-something on AMC 10 (cutoff mid 90's) and got 37 on MATHCOUNTS chapter
Z K Y
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Airbus320-214
77 posts
Airbus320-214
#4 h  Mar 3, 2025, 3:07 AM
Y by
Practice past problems of amc 10/12
Z K Y
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nxchman
21 posts
nxchman
#5 h  Mar 3, 2025, 9:09 PM
Y by
BAM10 wrote:
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?

Im in the same boat lol. Im in 8th grade and I never took amc 10, but this year I got 22 on amc 8.
Z K Y
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iwillregretthisnamelater
1 post
iwillregretthisnamelater
#6 h  Today at 1:59 AM
Y by
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard
Z K Y
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sadas123
1040 posts
sadas123
#7 h  Today at 2:04 AM
Y by
iwillregretthisnamelater wrote:
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard

Same except I am a 6th grader that got 24 on AMC 8 and a 37 on mathcounts chapter :(
Z K Y
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jb2015007
1698 posts
jb2015007
#8 h  Today at 2:09 AM
Y by
orangebear wrote:
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.

bruh i got a 51 on AMC 10 and got a 35 on mc chapter
(im better now relax im mocking 90+)
Z K Y
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ChickensEatGrass
26 posts
ChickensEatGrass
#9 h  Today at 2:19 AM
Y by
I'm an 8th grader and I got 25 on amc8 but only 40 on chapter, I made aime barely this year but I got like problem 4 wrong on 10a :wallbash_red:
so yes with your stats you have a decent chance, just study more and do past mocks, you can find them here on aops.
try to aim for at least 100. This year's cutoff for 10a was really low (94.5) but most years it's higher.
because you are in alg2, I'd recommend doing some geometry because there are several of those problems. maybe also start trig because they can provide faster solutions to them. but alg2 is a good start.
And make sure to not make sillies!!!!!!!!!! but I cant rlly say anything about that because i myself make 100000000 sillies every day :whistling:
Z K Y
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giratina3
432 posts
giratina3
#10 h  Today at 11:35 AM
Y by
I’m somebody who got 41 on chapter and 21 on AMC8 but didn’t qualify for AIME :stretcher:
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hashbrown2009
103 posts
hashbrown2009
#11 h  4 hours ago
Y by
Honestly it depends
I qualified for AIME in 5th grade (9th grade now) with 106.5
but that year I got like 16 on AMC8 lol I sold
also I pre-prepped for MathCounts and did mocks
averaged like 36-40
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Andyluo
850 posts
Andyluo
#12 h  an hour ago
Y by
Both completely different skill sets

my scores last year were

AMC 8: 17
chapter: 41 (My MATHCOUNTS skills were more developed)
AMC 10: 81

This year:

AMC 8: 21
Chapter: 43
AMC 10: 135

imo just take mocks + learn the theory from aops
mathdash good too
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