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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)!

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[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]
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0 replies
jlacosta
May 1, 2025
0 replies
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4th grader qual JMO
HCM2001   49
N Today at 4:05 PM by mathkiddus
i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
49 replies
HCM2001
May 22, 2025
mathkiddus
Today at 4:05 PM
J
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D1040 : A general and strange result
Dattier   0
Today at 12:46 PM
Source: les dattes à Dattier
Let $f \in C([0,1];[0,1])$ bijective, $f(0)=0$ and $(a_k) \in [0,1]^\mathbb N$ with $ \sum \limits_{k=0}^{+\infty} a_k$ converge.

Is it true that $\sum \limits_{k=0}^{+\infty} \sqrt{f(a_k)\times f^{-1}(a_k)}$ converge?
0 replies
Dattier
Today at 12:46 PM
0 replies
J
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Trigo or Complex no.?
hzbrl   6
N Today at 11:42 AM by GreenKeeper
(a) Let $y=\cos \phi+\cos 2 \phi$, where $\phi=\frac{2 \pi}{5}$. Verify by direct substitution that $y$ satisfies the quadratic equation $2 y^2=3 y+2$ and deduce that the value of $y$ is $-\frac{1}{2}$.
(b) Let $\theta=\frac{2 \pi}{17}$. Show that $\sum_{k=0}^{16} \cos k \theta=0$
(c) If $z=\cos \theta+\cos 2 \theta+\cos 4 \theta+\cos 8 \theta$, show that the value of $z$ is $-(1-\sqrt{17}) / 4$.



I could solve (a) and (b). Can anyone help me with the 3rd part please?
6 replies
hzbrl
May 27, 2025
GreenKeeper
Today at 11:42 AM
J
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AIME qual outside US?
daijobu   10
N Today at 5:23 AM by Yiyj
Can students outside the US take the AIME if they earn a qualifying score?
10 replies
daijobu
Yesterday at 7:10 PM
Yiyj
Today at 5:23 AM
J
H
Handouts/Resources on Limits.
Saucepan_man02   0
Today at 3:54 AM
Could anyone kindly share some resources/handouts on limits?
0 replies
Saucepan_man02
Today at 3:54 AM
0 replies
J
H
[$10K+ IN PRIZES] Poolesville Math Tournament (PVMT) 2025
qwerty123456asdfgzxcvb   20
N Today at 2:13 AM by panda2018
Hi everyone!

After the resounding success of the first three years of PVMT, the Poolesville High School Math Team is excited to announce the fourth annual Poolesville High School Math Tournament (PVMT)! The PVMT team includes a MOPper and multiple USA(J)MO and AIME qualifiers!

PVMT is open to all 6th-9th graders in the country (including rising 10th graders). Students will compete in teams of up to 4 people, and each participant will take three subject tests as well as the team round. The contest is completely free, and will be held virtually on June 7, 2025, from 10:00 AM to 4:00 PM (EST).

Additionally, thanks to our sponsors, we will be awarding approximately $10K+ worth of prizes (including gift cards, Citadel merch, AoPS coupons, Wolfram licenses) to top teams and individuals. More details regarding the actual prizes will be released as we get closer to the competition date.

Further, newly for this year we might run some interesting mini-events, which we will announce closer to the competition date, such as potentially a puzzle hunt and integration bee!

If you would like to register for the competition, the registration form can be found at https://pvmt.org/register.html or https://tinyurl.com/PVMT25.

Additionally, more information about PVMT can be found at https://pvmt.org

If you have any questions not answered in the below FAQ, feel free to ask in this thread or email us at falconsdomath@gmail.com!

We look forward to your participation!

FAQ
20 replies
qwerty123456asdfgzxcvb
Apr 5, 2025
panda2018
Today at 2:13 AM
J
H
Expression is a Cube
nosaj   38
N Today at 1:42 AM by NicoN9
Source: 2015 AIME I Problem 3
There is a prime number $p$ such that $16p+1$ is the cube of a positive integer. Find $p$.
38 replies
nosaj
Mar 20, 2015
NicoN9
Today at 1:42 AM
J
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IMC 1994 D2 P1
j___d   13
N Yesterday at 11:20 PM by krigger
Let $f\in C^1[a,b]$, $f(a)=0$ and suppose that $\lambda\in\mathbb R$, $\lambda >0$, is such that
$$|f'(x)|\leq \lambda |f(x)|$$for all $x\in [a,b]$. Is it true that $f(x)=0$ for all $x\in [a,b]$?
13 replies
j___d
Mar 6, 2017
krigger
Yesterday at 11:20 PM
J
H
D1039 : A strange and general result on series
Dattier   0
Yesterday at 10:33 PM
Source: les dattes à Dattier
Let $f \in C([0,1];[0,1])$ bijective, $f(0)=0$ and $(a_k) \in [0,1]^\mathbb N$ with $ \sum \limits_{k=0}^{+\infty} a_k$ converge.

Is it true that $\sum \limits_{k=0}^{+\infty} f(a_k)\times f^{-1}(a_k)$ converge?
0 replies
Dattier
Yesterday at 10:33 PM
0 replies
J
H
Aproximate ln(2) using perfect numbers
YLG_123   5
N Yesterday at 8:55 PM by ei_killua_
Source: Brazilian Mathematical Olympiad 2024, Level U, Problem 1
A positive integer \(n\) is called perfect if the sum of its positive divisors \(\sigma(n)\) is twice \(n\), that is, \(\sigma(n) = 2n\). For example, \(6\) is a perfect number since the sum of its positive divisors is \(1 + 2 + 3 + 6 = 12\), which is twice \(6\). Prove that if \(n\) is a positive perfect integer, then:
\[ \sum_{p|n} \frac{1}{p + 1} < \ln 2 < \sum_{p|n} \frac{1}{p - 1} \]where the sums are taken over all prime divisors \(p\) of \(n\).
5 replies
YLG_123
Oct 12, 2024
ei_killua_
Yesterday at 8:55 PM
J
H
Quadruple Binomial Coefficient Sum
P162008   4
N Yesterday at 8:40 PM by vmene
Source: Self made by my Elder brother
$\sum_{p=0}^{\infty} \sum_{r=0}^{\infty} \sum_{q=1}^{\infty} \sum_{s=0}^{p+q - 1} \frac{((-1)^{p+r+s+1})(2^{p+q-1}) \binom{p + q - s - 1}{p + q - 2s - 1}}{4^s(2p^2q + 2pqr + pq + qr)(2p + 2q + 2r + 3)}.$
4 replies
P162008
May 29, 2025
vmene
Yesterday at 8:40 PM
J
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IMC 1994 D1 P5
j___d   5
N Yesterday at 5:39 PM by krigger
a) Let $f\in C[0,b]$, $g\in C(\mathbb R)$ and let $g$ be periodic with period $b$. Prove that $\int_0^b f(x) g(nx)\,\mathrm dx$ has a limit as $n\to\infty$ and
$$\lim_{n\to\infty}\int_0^b f(x)g(nx)\,\mathrm dx=\frac 1b \int_0^b f(x)\,\mathrm dx\cdot\int_0^b g(x)\,\mathrm dx$$
b) Find
$$\lim_{n\to\infty}\int_0^\pi \frac{\sin x}{1+3\cos^2nx}\,\mathrm dx$$
5 replies
j___d
Mar 6, 2017
krigger
Yesterday at 5:39 PM
J
H
Putnam 2019 A1
awesomemathlete   33
N Yesterday at 3:25 PM by cursed_tangent1434
Source: 2019 William Lowell Putnam Competition
Determine all possible values of $A^3+B^3+C^3-3ABC$ where $A$, $B$, and $C$ are nonnegative integers.
33 replies
awesomemathlete
Dec 10, 2019
cursed_tangent1434
Yesterday at 3:25 PM
J
H
IMC 1994 D1 P2
j___d   5
N Yesterday at 3:11 PM by krigger
Let $f\in C^1(a,b)$, $\lim_{x\to a^+}f(x)=\infty$, $\lim_{x\to b^-}f(x)=-\infty$ and $f'(x)+f^2(x)\geq -1$ for $x\in (a,b)$. Prove that $b-a\geq\pi$ and give an example where $b-a=\pi$.
5 replies
j___d
Mar 6, 2017
krigger
Yesterday at 3:11 PM
J
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J
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k RIP BS2012
gavinhaominwang   22
N Apr 23, 2025 by torch
Rip BS2012, I hope you come back next year stronger and prove everyone wrong.
22 replies
gavinhaominwang
Apr 23, 2025
torch
Apr 23, 2025
J
RIP BS2012
G H J
Reveal topic tags
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G H BBookmark kLocked kLocked NReply
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gavinhaominwang
92 posts
gavinhaominwang
#1 h  Apr 23, 2025, 12:32 AM • 4 Y
Y by PikaPika999, bwu_2022, scannose, bjump
Rip BS2012, I hope you come back next year stronger and prove everyone wrong.
Z Y
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maxamc
586 posts
maxamc
#2 h  Apr 23, 2025, 12:33 AM • 1 Y
Y by PikaPika999
Also rip hashbrown2009
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Andyluo
1008 posts
Andyluo
#3 h  Apr 23, 2025, 2:43 AM • 4 Y
Y by Mathandski, bjump, megarnie, KevinYang2.71
RIP Bjump, you got this next year tho fr
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mathkiddus
243 posts
mathkiddus
#4 h  Apr 23, 2025, 2:55 AM • 2 Y
Y by mathfan2020, bjump
also RIP dogeA,
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vincentwant
1446 posts
vincentwant
#5 h  Apr 23, 2025, 3:36 AM • 3 Y
Y by mathfan2020, Ilikeminecraft, bjump
RIP a_smart_alecks
Z Y
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ThoughtfulGorilla10
27 posts
ThoughtfulGorilla10
#6 h  Apr 23, 2025, 3:40 AM
Y by
What do i do here
Z Y
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mathfan2020
351 posts
mathfan2020
#7 h  Apr 23, 2025, 3:56 AM • 1 Y
Y by bjump
RIP PenguinMoosey
Z Y
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PEKKA
1850 posts
PEKKA
#8 h  Apr 23, 2025, 4:23 AM • 1 Y
Y by bjump
RIP llmmddtt1
Z Y
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zhoujef000
322 posts
zhoujef000
#9 h  Apr 23, 2025, 4:26 AM • 4 Y
Y by bjump, megarnie, mathfan2020, KnowingAnt
RIP KnowingAnt
Z Y
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Alpaca31415
12 posts
Alpaca31415
#10 h  Apr 23, 2025, 4:41 AM • 1 Y
Y by bjump
rip me fr I suck
Z Y
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Ilikeminecraft
674 posts
Ilikeminecraft
#11 h  Apr 23, 2025, 4:55 AM • 2 Y
Y by bjump, mathfan2020
rip impromptuA
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deduck
237 posts
deduck
#12 h  Apr 23, 2025, 5:24 AM • 4 Y
Y by bjump, bachkieu, mathfan2020, ninjaforce
rip math4life2020
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KevinYang2.71
428 posts
KevinYang2.71
#13 h  Apr 23, 2025, 6:40 AM • 4 Y
Y by Mathandski, bjump, megarnie, deduck
rip deduck
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MathRook7817
751 posts
MathRook7817
#14 h  Apr 23, 2025, 2:16 PM
Y by
RIP MathRook7817
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NoSignOfTheta
1749 posts
NoSignOfTheta
#15 h  Apr 23, 2025, 2:23 PM
Y by
RIP aopsonline2020888
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ethan2011
352 posts
ethan2011
#16 h  Apr 23, 2025, 2:28 PM • 1 Y
Y by mathfan2020
RIP mathfan2020
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TiguhBabeHwo
489 posts
TiguhBabeHwo
#17 h  Apr 23, 2025, 2:50 PM • 1 Y
Y by mathfan2020
RIP ethan2011
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MathPerson12321
3796 posts
MathPerson12321
#18 h  Apr 23, 2025, 2:53 PM
Y by
rip everyone but we dont need a separate thread for this
/req lock

you all will make it next yr!
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bachkieu
137 posts
bachkieu
#19 h  Apr 23, 2025, 3:01 PM
Y by
rip tiguhbabehwo 232
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Mathdreams
1472 posts
Mathdreams
#20 h  Apr 23, 2025, 3:13 PM • 1 Y
Y by bjump
RIP bjump :(
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dragoon
1947 posts
dragoon
#21 h  Apr 23, 2025, 3:14 PM • 1 Y
Y by bjump
rip bjump :( :(
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MathRook7817
751 posts
MathRook7817
#22 h  Apr 23, 2025, 3:22 PM
Y by
RIP everyone who didnt make JMO (me)
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torch
1016 posts
torch
#23 h  Apr 23, 2025, 3:23 PM • 2 Y
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rip bjump :(
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