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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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0 replies
jlacosta
Apr 2, 2025
0 replies
J
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Some nice summations
amitwa.exe   31
N a few seconds ago by soryn
Problem 1: $\Omega=\left(\sum_{0\le i\le j\le k}^{\infty} \frac{1}{3^i\cdot4^j\cdot5^k}\right)\left(\mathop{{\sum_{i=0}^{\infty}\sum_{j=0}^{\infty}\sum_{k=0}^{\infty}}}_{i\neq j\neq k}\frac{1}{3^i\cdot3^j\cdot3^k}\right)=?$
31 replies
amitwa.exe
May 24, 2024
soryn
a few seconds ago
J
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Interesting inequalities
sqing   0
18 minutes ago
Source: Own
Let $ a,b,c\geq 0 ,b+c-ca=1 $ and $ c+a-ab=3.$ Prove that
$$a+\frac{19}{10}b-bc\leq 2-\sqrt 2$$$$a+\frac{17}{10}b+c-bc\leq 3$$$$ a^2+\frac{9}{5}b-bc\leq 6-4\sqrt 2$$$$ a^2+\frac{8}{5}b^2-bc\leq 6-4\sqrt 2$$$$a+1.974873b-bc\leq 2-\sqrt 2$$$$a+1.775917b+c-bc\leq 3$$

0 replies
sqing
18 minutes ago
0 replies
J
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Two permutations
Nima Ahmadi Pour   12
N 43 minutes ago by Zhaom
Source: Iran prepration exam
Suppose that $ a_1$, $ a_2$, $ \ldots$, $ a_n$ are integers such that $ n\mid a_1 + a_2 + \ldots + a_n$.
Prove that there exist two permutations $ \left(b_1,b_2,\ldots,b_n\right)$ and $ \left(c_1,c_2,\ldots,c_n\right)$ of $ \left(1,2,\ldots,n\right)$ such that for each integer $ i$ with $ 1\leq i\leq n$, we have
\[ n\mid a_i - b_i - c_i \]

Proposed by Ricky Liu & Zuming Feng, USA
12 replies
Nima Ahmadi Pour
Apr 24, 2006
Zhaom
43 minutes ago
J
H
Easy Number Theory
math_comb01   37
N an hour ago by John_Mgr
Source: INMO 2024/3
Let $p$ be an odd prime and $a,b,c$ be integers so that the integers $$a^{2023}+b^{2023},\quad b^{2024}+c^{2024},\quad a^{2025}+c^{2025}$$are divisible by $p$.
Prove that $p$ divides each of $a,b,c$.
$\quad$
Proposed by Navilarekallu Tejaswi
37 replies
math_comb01
Jan 21, 2024
John_Mgr
an hour ago
J
No more topics!
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J
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Regarding Maaths olympiad prepration
omega2007   13
N Apr 5, 2025 by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compiled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your perspective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
13 replies
omega2007
Apr 4, 2025
omega2007
Apr 5, 2025
J
Regarding Maaths olympiad prepration
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
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omega2007
10 posts
omega2007
#1 h  Apr 4, 2025, 3:13 PM
Y by
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compiled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your perspective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
This post has been edited 1 time. Last edited by omega2007, Apr 5, 2025, 2:48 AM
Reason: Spelling error
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GreekIdiot
174 posts
GreekIdiot
#2 h  Apr 4, 2025, 3:46 PM • 1 Y
Y by omega2007
Sure... Try Chen's EGMO and Khurmi's MONT. Great books and very thorough, albeit extremely challenging at some points. Keep in mind to study in an organized manner, not learning random interesting theorems. Im at your age too and this is something I have personally struggled with, thats why I am mentioning it.
You can find them online easily in pdf format, but I suggest printing the books or buying them. Helps me study a lot more.
This post has been edited 1 time. Last edited by GreekIdiot, Apr 4, 2025, 3:47 PM
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omega2007
10 posts
omega2007
#3 h  Apr 5, 2025, 2:40 AM
Y by
Thanks for your support.
EGMO AND MONT I HAVE SOLVE ALREADY
In Aops things are not arranged //
So I need this things
But do you have compiled resources

Like >>>> List of books
List of handouts
Pdf
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MathleteMystic
7 posts
MathleteMystic
#4 h  Apr 5, 2025, 5:44 AM
Y by
omega2007 wrote:
Thanks for your support.
EGMO AND MONT I HAVE SOLVE ALREADY
In Aops things are not arranged //
So I need this things
But do you have compiled resources

Like >>>> List of books
List of handouts
Pdf

Didn't u say u r starting ur preparation from scratch..??..I don't think it can be called starting from scratch if u hv already solved those 2 books :|
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omega2007
10 posts
omega2007
#5 h  Apr 5, 2025, 5:53 AM
Y by
Yeah

Don't you have compiled resources
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Captainscrubz
57 posts
Captainscrubz
#6 h  Apr 5, 2025, 8:16 AM • 1 Y
Y by MrdiuryPeter
Visit evan chens website theres all material and resources you need
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mikkymini2
13 posts
mikkymini2
#7 h  Apr 5, 2025, 8:38 AM
Y by
Hi, this is a separate doubt.. But how did you guys start with EGMO? Like do I just pick up the book and start solving if my Geo basics are good or do I cover other supplement materials before I start with this? And lastly how do I proceed if I am stuck with a question (and preferably could you explain how you guys overcame that)...To my knowledge some hints and some solutions are provided, they often require so much effort to try on your own :wacko:
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omega2007
10 posts
omega2007
#8 h  Apr 5, 2025, 8:43 AM
Y by
It totally depends on your understanding
Like in case of geometry
Are your basic clear for example are you familiar
and can you proof theorems of class 8,9,10,11,12 maths ( geometry section) >>> if yes >> than you can proceed with EGMO> GRASP THEORY and solve problems.

Here are some resources for geometry
Geometry Resources
Euclidean Geometry in Mathematical Olympiads - Evan Chen - Both book - good book. By far the greatest geometry book to prepare for olympiads. if you had to choose one book, its definitely this one
Muricaa- It is book/handout discussing popular configs in geo mostly pointed out to be well-known by aops-ers. It has 100 problems at the end with roughly the difficulty increasing as you move forward. It can be found here
Handouts on Projective Geometry and Moving Points A really nice handout written by Rohan Goyal, starting from basics and going upto nukes like DIT and DDIT can be found here. Another nice handout on learning the method of moving points and it's application in problems can be found here
AOPS Geo Mocks: https://artofproblemsolving.com/community/c1668102_aops_geo_mocks
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omega2007
10 posts
omega2007
#9 h  Apr 5, 2025, 8:45 AM
Y by
mikkymini2 wrote:
Hi, this is a separate doubt.. But how did you guys start with EGMO? Like do I just pick up the book and start solving if my Geo basics are good or do I cover other supplement materials before I start with this? And lastly how do I proceed if I am stuck with a question (and preferably could you explain how you guys overcame that)...To my knowledge some hints and some solutions are provided, they often require so much effort to try on your own :wacko:

For questions solving I guess you can use AI like chat gpt and my favourite deepseek
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mikkymini2
13 posts
mikkymini2
#10 h  Apr 5, 2025, 8:56 AM • 1 Y
Y by omega2007
@omega, thx for the help, I will look into those books. Will try using AI in the future, I did not try it before thinking they would have been inaccurate for challenging math problems...
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omega2007
10 posts
omega2007
#11 h  Apr 5, 2025, 9:00 AM
Y by
Do you all compiled resources which are shared on Aops for maths olympiad
Like handouts , books like that
Because there are many .....
I want in one place compiled so that I can use

I hope someone will give me
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kjhgyuio
50 posts
kjhgyuio
#12 h  Apr 5, 2025, 9:09 AM
Y by
omega2007 wrote:
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compiled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your perspective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.

i also want to ask the same but for 8th grade
This post has been edited 1 time. Last edited by kjhgyuio, Apr 5, 2025, 9:11 AM
Reason: nil
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mikkymini2
13 posts
mikkymini2
#13 h  Apr 5, 2025, 9:37 AM
Y by
I think you could try this...
https://artofproblemsolving.com/community/c13_contest_collections
It has complied questions for various Olympiads PYQs
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omega2007
10 posts
omega2007
#14 h  Apr 5, 2025, 9:48 AM
Y by
I don't need pyq
I need olympiad articles
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