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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Tuesday at 2:14 PM
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
and train with the best! Please note that early bird pricing ends August 19th!
Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
All classes start 7:30pm ET/4:30pm PT unless otherwise noted.

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0 replies
jwelsh
Tuesday at 2:14 PM
0 replies
Interesting problem
Tricky123   6
N 3 hours ago by gator333
Q) which is bigger:-
1. $e^{\pi}$ or $\pi^{e}$
2. $e^{\frac{1}{\pi}}$ or $\pi^{\frac{1}{e}}$
3. $\pi^{\pi}$ or $e^{e}$
4. $\pi^{\frac{1}{\pi}}$ or $e^{\frac{1}{e}}$

How to make a easy progress. If there is any new process please help me.
6 replies
Tricky123
Yesterday at 2:53 AM
gator333
3 hours ago
nth root of a, b in O(sqrt(n))
tenniskidperson3   63
N Yesterday at 9:29 PM by ihategeo_1969
Source: 2014 USAMO problem 6
Prove that there is a constant $c>0$ with the following property: If $a, b, n$ are positive integers such that $\gcd(a+i, b+j)>1$ for all $i, j\in\{0, 1, \ldots n\}$, then\[\min\{a, b\}>c^n\cdot n^{\frac{n}{2}}.\]
63 replies
1 viewing
tenniskidperson3
Apr 30, 2014
ihategeo_1969
Yesterday at 9:29 PM
Sad Combinatorics II
tastymath75025   26
N Yesterday at 9:13 PM by ray66
Source: 2018 USAMO 6, by Richard Stong
Let $a_n$ be the number of permutations $(x_1, x_2, \dots, x_n)$ of the numbers $(1,2,\dots, n)$ such that the $n$ ratios $\frac{x_k}{k}$ for $1\le k\le n$ are all distinct. Prove that $a_n$ is odd for all $n\ge 1$.

Proposed by Richard Stong
26 replies
tastymath75025
Apr 19, 2018
ray66
Yesterday at 9:13 PM
Sad Combinatorics
62861   109
N Yesterday at 8:56 PM by ray66
Source: USAMO 2018 P4 and JMO 2018 P5, by Ankan Bhattacharya
Let $p$ be a prime, and let $a_1, \dots, a_p$ be integers. Show that there exists an integer $k$ such that the numbers
\[a_1 + k, a_2 + 2k, \dots, a_p + pk\]produce at least $\tfrac{1}{2} p$ distinct remainders upon division by $p$.

Proposed by Ankan Bhattacharya
109 replies
62861
Apr 19, 2018
ray66
Yesterday at 8:56 PM
Goals for 2025-2026
Airbus320-214   287
N Yesterday at 8:21 PM by ouia1234
Please write down your goal/goals for competitions here for 2025-2026.
287 replies
Airbus320-214
May 11, 2025
ouia1234
Yesterday at 8:21 PM
real analysis intermediate concepts
am_11235...   4
N Yesterday at 7:32 PM by Moubinool
Source: AMM, proposed by Cezar Lupu and Tudorel Lupu
Let $f$ be a positive-valued, concave function on $[0,1]$. Prove that $$\frac34\left(\int_0^1f(x)\,dx\right)^2\leq\frac18+\int_0^1f^3(x)\,dx$$
4 replies
am_11235...
Tuesday at 11:02 AM
Moubinool
Yesterday at 7:32 PM
real analysis problem
TSyyh666   4
N Yesterday at 4:21 PM by TSyyh666
Source: BNU entrance exam
Let $E$ be a Lebesgue measurable set, and let $ f, g \in L(E)$ and $f_k, g_k \in L(E) $ for each $ k \in \mathbb{N} . $Assume there exists a constant $M$ such that $|f_k(x)| \leq M$ for all $k \in \mathbb{N}$ and $x \in E $, and that $$\lim_{k \to \infty} \int_E |f_k(x) - f(x)| \, \mathrm{d}x = 0$$and $$\lim_{k \to \infty} \int_E |g_k(x) - g(x)| \, \mathrm{d}x = 0 . $$Prove that$$\lim_{k \to \infty} \int_E \big| f_k(x)g_k(x) - f(x)g(x) \big| \, \mathrm{d}x = 0.$$
4 replies
TSyyh666
Yesterday at 7:22 AM
TSyyh666
Yesterday at 4:21 PM
Nr.roots of an equation with abs.values
flip2004   1
N Yesterday at 2:01 PM by Mathzeus1024
Source: ALEX collection
If $A, B$ are real numbers, how many roots has the equation $\; \; \left|\left||x-1|-2\right|-3\right|=Ax+B \; \; \; ,\; \; x\in {\mathbb R}\; \;$ ?
1 reply
flip2004
Aug 25, 2004
Mathzeus1024
Yesterday at 2:01 PM
analysis
ay19bme   0
Yesterday at 12:06 PM
.........................
0 replies
ay19bme
Yesterday at 12:06 PM
0 replies
real analysis difficult concepts
am_11235...   0
Yesterday at 10:14 AM
Source: AMM, proposed by Cesar Adolfo Hernandez Melo
Let $f$ be a convex, continuously differentiable function from $[1,\infty)$ to $\mathbb{R}$ such that $f'(x)>0$ for all $x\geq1$. Prove that the improper integral $\int_1^\infty\frac{dx}{f'(x)}$ is convergent if and only if the series $\sum_{n=1}^\infty\left(f^{-1}(f(n)+\epsilon)-n\right)$ is convergent for all $\epsilon>0$.
0 replies
am_11235...
Yesterday at 10:14 AM
0 replies
real analysis difficult concepts
am_11235...   2
N Yesterday at 9:44 AM by Ritwin
Source: AMM, proposed by Oleksiy Klurman
Let $f$ be a continuous function from $[0,1]$ into $\mathbb{R}^+$. Prove that $$\int_0^1f(x)\,dx-\exp\left[\int_0^1\log f(x)\,dx\right]\leq\max_{0\leq x,y\leq1}\left(\sqrt{f(x)}-\sqrt{f(y)}\right)^2$$
2 replies
am_11235...
Tuesday at 2:12 PM
Ritwin
Yesterday at 9:44 AM
Indefinite Integration
jonny   2
N Tuesday at 2:10 PM by Mathzeus1024
Finding $\int\frac{x^2}{(x+2)^2\cdot (x+4)^2}dx$
2 replies
jonny
Sep 18, 2018
Mathzeus1024
Tuesday at 2:10 PM
linear algebra difficult concepts
am_11235...   0
Tuesday at 10:38 AM
Source: AMM, proposed by Daniel Goffinet
$(a)$ Prove that a (square) matrix over a field $F$ is singular if and only if it is a product of nilpotent matrices.

$(b)$ If $F=\mathbb{C}$, prove that the number of nilpotent factors can be bounded independently of the size of the matrix.
0 replies
am_11235...
Tuesday at 10:38 AM
0 replies
Graph a function by hand using first and second derivatives
bunny321   1
N Tuesday at 10:08 AM by Mathzeus1024
Graph $f(x) = 5x^{\frac{2}{3}} - x^{\frac{5}{3}}$ using the first and second derivatives. I need to know things such as x-int, y-int, symmetry, critical numbers, minimums and maximums, increasing and decreasing intervals, points of inflection, and concavity. Could someone please walk me through how to find these things? I needed to graph this function by hand for a quiz and I had a really hard time. Thanks!
1 reply
bunny321
Apr 12, 2023
Mathzeus1024
Tuesday at 10:08 AM
USAMO Medals
YauYauFilter   54
N May 9, 2025 by ohiorizzler1434
YauYauFilter
Apr 24, 2025
ohiorizzler1434
May 9, 2025
USAMO Medals
G H J
G H BBookmark kLocked kLocked NReply
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N3bula
312 posts
#41
Y by
Inaaya wrote:

u guys need to learn about maths people beyond the aops celebrities bro
ik bro u mean like actual adults
like 3b1b and matt parker and ben orlin
oh yeah and our glorious king richard[/quote]

No not even adults bro like even amongst oly people
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Inaaya
445 posts
#42
Y by
ohiorizzler1434 wrote:
Inaaya have you even heard of Terence Tao? How could you neglect to mention Terence Tao. It really reflects the problem of AoPS's disconnect from real maths.

But let's get back on point! Amazing job all the USAMO participants! Let's embrace this amazing olympiad journey!

i am not even close to oly level but whatever
in my mind, the people that i listed make math content for the general audience, while most of the stuff terrence tao makes is targeted toward oly qual or above
mb guys!!
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a_smart_alecks
56 posts
#43 • 1 Y
Y by dolphinday
there's a lot of cracked aopsers, but one common thread that unites them is that they don't like having a bunch of people on aops borderline worshipping them :/ making a blog specifically dedicated to one child is kinda creepy... it's good to have role models but please don't take it too far

anyways, congrats to all oly takers!! :$ $D
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Inaaya
445 posts
#44
Y by
a_smart_alecks wrote:
there's a lot of cracked aopsers, but one common thread that unites them is that they don't like having a bunch of people on aops borderline worshipping them :/ making a blog specifically dedicated to one child is kinda creepy... it's good to have role models but please don't take it too far

anyways, congrats to all oly takers!! :$ $D

cough cough redfiretruck cough cough
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mhgelgi
843 posts
#46
Y by
Tralalero wrote:
Another day another Inaaya glaze. Why is your whole online persona centered around treating AoPSers like gods? Hop off.

... says an alt who just hops in two days ago :alien:
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Inaaya
445 posts
#47
Y by
Tralalero wrote:
Another day another Inaaya glaze. Why is your whole online persona centered around treating AoPSers like gods? Hop off.

who even are you
do i know you
also says the person who literally made a brainrot username
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ZMB038
445 posts
#48
Y by
Inaaya wrote:
Tralalero wrote:
Another day another Inaaya glaze. Why is your whole online persona centered around treating AoPSers like gods? Hop off.

who even are you
do i know you
also says the person who literally made a brainrot username

Inaaya don’t listen to them. They’re just dumb, besides this is Channing glaze forum. Look at the tags.
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Inaaya
445 posts
#49
Y by
ZMB038 wrote:
Inaaya wrote:
Tralalero wrote:
Another day another Inaaya glaze. Why is your whole online persona centered around treating AoPSers like gods? Hop off.

who even are you
do i know you
also says the person who literally made a brainrot username

Inaaya don’t listen to them. They’re just dumb, besides this is Channing glaze forum. Look at the tags.

bro don't leave out the other amo medal winners :(
This is a glaze post for all the collective amo takers and winners
All amosers deserve adequate glaze!! not just channing!!!
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DreamineYT
301 posts
#50 • 1 Y
Y by PikaPika999
imagine being so orz that you mop but cant go to mop(cough cough krithik)
This post has been edited 1 time. Last edited by DreamineYT, May 8, 2025, 11:10 PM
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Pengu14
651 posts
#51 • 1 Y
Y by PikaPika999
DreamineYT wrote:
imagine being so orz that you mop but cant go to mop(cough cough krithik)

(cough cough advait)
(cough cough tiger)
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ConfidentKoala4
613 posts
#52 • 1 Y
Y by PikaPika999
is advait even on the lhigh team anymore
or was he too orz for it
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vincentwant
1473 posts
#53
Y by
vincentwant wrote:
I believe last year Channing did not mop because the test papers got lost or something

ok so i mixed up the years, channing's test papers got lost in 2023 not 2024, and they did get graded eventually
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NoSignOfTheta
1759 posts
#54 • 1 Y
Y by Math4Life2020
He took 2 business days to respond :rotfl:
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Pengu14
651 posts
#55
Y by
bro pulled up to Channing rq
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ohiorizzler1434
886 posts
#56 • 1 Y
Y by Exponent11
Bruh! I'm a big fan of Channing too! Channing is the ORZ sigma who ADMITS!
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