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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:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
Is EGMO good for JMO Geometry Questions?
MathRook7817   2
N 6 hours ago by CatCatHead
Hi guys, I was just wondering if EGMO is a good book for JMO/AMO/olympiad level questions, or if there exists another olympiad geo book. Thanks!
2 replies
MathRook7817
Today at 3:05 AM
CatCatHead
6 hours ago
geometry
JetFire008   1
N Today at 4:23 AM by ohiorizzler1434
Given four concyclic points. For each subset of three points take the incenter. Show that the four incentres form a rectangle.
1 reply
JetFire008
Yesterday at 4:14 PM
ohiorizzler1434
Today at 4:23 AM
A pentagon inscribed in a circle of radius √2
tom-nowy   2
N Today at 4:20 AM by ohiorizzler1434
Can a pentagon with all rational side lengths be inscribed in a circle of radius $\sqrt{2}$ ?
2 replies
tom-nowy
Today at 2:37 AM
ohiorizzler1434
Today at 4:20 AM
Inequalities
sqing   8
N Today at 3:12 AM by sqing
Let $ a,b,c>0 $ and $ a+b\leq 16abc. $ Prove that
$$ a+b+kc^3\geq\sqrt[4]{\frac{4k} {27}}$$$$ a+b+kc^4\geq\frac{5} {8}\sqrt[5]{\frac{k} {2}}$$Where $ k>0. $
$$ a+b+3c^3\geq\sqrt{\frac{2} {3}}$$$$ a+b+2c^4\geq \frac{5} {8}$$
8 replies
sqing
Sunday at 12:46 PM
sqing
Today at 3:12 AM
purple comet discussion
ConfidentKoala4   64
N Today at 3:11 AM by MathCosine
when can we discuss purple comet
64 replies
ConfidentKoala4
May 2, 2025
MathCosine
Today at 3:11 AM
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   70
N Today at 3:00 AM by stuffedmath
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary


Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


70 replies
audio-on
Jan 26, 2025
stuffedmath
Today at 3:00 AM
USAMO Medals
YauYauFilter   20
N Today at 2:38 AM by vincentwant
YauYauFilter
Apr 24, 2025
vincentwant
Today at 2:38 AM
trapezoid
Darealzolt   0
Today at 2:03 AM
Let \(ABCD\) be a trapezoid such that \(A, B, C, D\) lie on a circle with center \(O\), and side \(AB\) is parallel to side \(CD\). Diagonals \(AC\) and \(BD\) intersect at point \(M\), and \(\angle AMD = 60^\circ\). It is given that \(MO = 10\). It is also known that the difference in length between \(AB\) and \(CD\) can be expressed in the form \(m\sqrt{n}\), where \(m\) and \(n\) are positive integers and \(n\) is square-free. Compute the value of \(m + n\).
0 replies
Darealzolt
Today at 2:03 AM
0 replies
Inequalities
sqing   2
N Today at 1:47 AM by sqing
Let $ a,b,c\geq 0 ,   2a +ab + 12a bc \geq 8. $ Prove that
$$  a+  (b+c)(a+1)+\frac{4}{5}  bc \geq 4$$$$  a+  (b+c)(a+0.9996)+ 0.77  bc \geq 4$$
2 replies
sqing
May 4, 2025
sqing
Today at 1:47 AM
anyone who can help me this 2 problems?
auroracliang   2
N Yesterday at 11:51 PM by ReticulatedPython
1. Let r be the radius of the largest circle which is tangent to the parabola y=x^2 at x=0 and which lies entirely on or inside (that is, above) the parabola, find r.

2. Counting number n has the following property,: if we take any 50 different numbers from 1,2,3, ... n, there always are two numbers with the difference of 7. what is the largest value among all value of n?


thanks a lot
2 replies
auroracliang
Nov 3, 2024
ReticulatedPython
Yesterday at 11:51 PM
What conic section is this? Is this even a conic section?
invincibleee   2
N Yesterday at 11:48 PM by ReticulatedPython
IMAGE

The points in this are given by
P = (sin2A, sin4A)∀A [0,2π]
Is this a conic section? what is this?
2 replies
invincibleee
Nov 15, 2024
ReticulatedPython
Yesterday at 11:48 PM
Spheres, ellipses, and cones
ReticulatedPython   0
Yesterday at 11:38 PM
A sphere is inscribed inside a cone with base radius $1$ and height $2.$ Another sphere of radius $r$ is internally tangent to the lateral surface of the cone, but does not intersect the larger inscribed sphere. A plane is tangent to both of these spheres, and passes through the inside of the cone. The intersection of the plane and the cone forms an ellipse. Find the maximum area of this ellipse.
0 replies
ReticulatedPython
Yesterday at 11:38 PM
0 replies
Looking for users and developers
derekli   13
N Yesterday at 11:31 PM by DreamineYT
Guys I've been working on a web app that lets you grind high school lvl math. There's AMCs, AIME, BMT, HMMT, SMT etc. Also, it's infinite practice so you can keep grinding without worrying about finding new problems. Please consider helping me out by testing and also consider joining our developer team! :P :blush:

Link: https://stellarlearning.app/competitive
13 replies
derekli
May 4, 2025
DreamineYT
Yesterday at 11:31 PM
trigonometric functions
VivaanKam   12
N Yesterday at 11:06 PM by aok
Hi could someone explain the basic trigonometric functions to me like sin, cos, tan etc.
Thank you!
12 replies
VivaanKam
Apr 29, 2025
aok
Yesterday at 11:06 PM
Modular Arithmetic Handout
MathCosine   18
N Apr 11, 2025 by nsking_1209
Hi everyone,

I recently created a handout on modular arithmetic for a local math club. I thought it would help quite a lot with understanding basic properties, as modular arithmetic is a very popular intermediate step in number theory problems, so I decided to leave it here as a resource for anyone who needs it. Feel free to share it around, and hope it helps!

Sincerely,
MathCosine
18 replies
MathCosine
Apr 7, 2025
nsking_1209
Apr 11, 2025
Modular Arithmetic Handout
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MathCosine
161 posts
#1 • 3 Y
Y by Awesome_Twin1, Pengu14, Sedro
Hi everyone,

I recently created a handout on modular arithmetic for a local math club. I thought it would help quite a lot with understanding basic properties, as modular arithmetic is a very popular intermediate step in number theory problems, so I decided to leave it here as a resource for anyone who needs it. Feel free to share it around, and hope it helps!

Sincerely,
MathCosine
Attachments:
Modular_Arithmetic_Intro_v1.pdf (137kb)
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jb2015007
1934 posts
#2
Y by
yeesssss ty i need this
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franklin2013
274 posts
#3
Y by
same for me tysm!
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Jaxman8
120 posts
#4
Y by
Is there an intermediate
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jb2015007
1934 posts
#5
Y by
pls make more! People like me need them!

also another suggestion is make them a tad longer other than that though, its amazing!
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sadas123
1261 posts
#6
Y by
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?
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sadas123
1261 posts
#7
Y by
sadas123 wrote:
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?

I am a bit rusty to number Theory srry
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mathprodigy2011
325 posts
#8
Y by
sadas123 wrote:
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?

Number of positive integers less than x which are relatively prime to x is known as eulers totient function or phi(x)
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Pengu14
600 posts
#9
Y by
mathprodigy2011 wrote:
sadas123 wrote:
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?

Number of positive integers less than x which are relatively prime to x is known as eulers totient function or phi(x)

ADMITS
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greenturtle3141
3558 posts
#10 • 2 Y
Y by scannose, Sedro
Quote:
$$9^{1012} \equiv (-1)^{1012}$$
This is not at all obvious based on what you've written thus far! This trick is too important to simply gloss over.
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lord_of_the_rook
154 posts
#11
Y by
One small nitpick: You say that $a | b$ if there exists $c$ such that $\frac b a = c$. However, we say that $0 | 0$, so I think a better definition would be that there exists some $c$ such that $b = ac$.
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fake123
93 posts
#12
Y by
greenturtle3141 wrote:
Quote:
$$9^{1012} \equiv (-1)^{1012}$$
This is not at all obvious based on what you've written thus far! This trick is too important to simply gloss over.

how? it's just the units digit
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MathCosine
161 posts
#13 • 1 Y
Y by lord_of_the_rook
lord_of_the_rook wrote:
One small nitpick: You say that $a | b$ if there exists $c$ such that $\frac b a = c$. However, we say that $0 | 0$, so I think a better definition would be that there exists some $c$ such that $b = ac$.

Thanks, I’ll update it soon.
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MathCosine
161 posts
#14
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Jaxman8 wrote:
Is there an intermediate

maybe I could… if this is really good, I could try to make another intermediate one for topics like quadratic reciprocity…
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Jaxman8
120 posts
#15
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Yes, this was a really good intro hand out. Thank you!
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idk12345678
392 posts
#16 • 1 Y
Y by franklin2013
MathCosine wrote:
Jaxman8 wrote:
Is there an intermediate

maybe I could… if this is really good, I could try to make another intermediate one for topics like quadratic reciprocity…

that would be really helpful
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MathCosine
161 posts
#17
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Jaxman8 wrote:
Yes, this was a really good intro hand out. Thank you!

Glad you enjoyed it! I'll get to an intermediate one soon.
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N3bula
268 posts
#18
Y by
MathCosine wrote:
Jaxman8 wrote:
Is there an intermediate

maybe I could… if this is really good, I could try to make another intermediate one for topics like quadratic reciprocity…

wtf is quadratic reciprocity is intermediate wtf is advanced nt just straight up analytic or algebraic nt like bro if ur pulling out cherbatov density in an exam ur trolling
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nsking_1209
172 posts
#19
Y by
binomial theorem and wilson's theorem can be used for mods as well
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