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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
J
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Fake number theory
Davdav1232   4
N a minute ago by NO_SQUARES
Source: Israel TST p1
For a positive integer \( n \geq 2 \), does there exist positive integer solutions to the following system of equations?

\[ \begin{cases} a^n - 2b^n = 1, \\ b^n - 2c^n = 1. \end{cases} \]
4 replies
Davdav1232
Dec 19, 2024
NO_SQUARES
a minute ago
J
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Inequality, inequality, inequality...
Assassino9931   2
N 5 minutes ago by pooh123
Source: Al-Khwarizmi Junior International Olympiad 2025 P6
Let $a,b,c$ be real numbers such that \[ab^2+bc^2+ca^2=6\sqrt{3}+ac^2+cb^2+ba^2.\]Find the smallest possible value of $a^2 + b^2 + c^2$.

Binh Luan and Nhan Xet, Vietnam
2 replies
Assassino9931
4 hours ago
pooh123
5 minutes ago
J
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Interesting inequalities
sqing   1
N 19 minutes ago by sqing
Source: Own
Let $ a,b,c\geq 0 , (a+k )(b+c)=k+1.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2k-3+2\sqrt{k+1}}{3k-1}$$Where $ k\geq \frac{2}{3}.$
Let $ a,b,c\geq 0 , (a+1)(b+c)=2.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq 2\sqrt{2}-1$$Let $ a,b,c\geq 0 , (a+3)(b+c)=4.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{7}{4}$$Let $ a,b,c\geq 0 , (3a+2)(b+c)= 5.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2(2\sqrt{15}-5)}{3}$$
1 reply
+1 w
sqing
20 minutes ago
sqing
19 minutes ago
J
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Prime sums of pairs
Assassino9931   1
N 24 minutes ago by Nuran2010
Source: Al-Khwarizmi Junior International Olympiad 2025 P5
Sevara writes in red $8$ distinct positive integers and then writes in blue the $28$ sums of each two red numbers. At most how many of the blue numbers can be prime?

Marin Hristov, Bulgaria
1 reply
+1 w
Assassino9931
4 hours ago
Nuran2010
24 minutes ago
J
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Is this true?
Entrepreneur   1
N an hour ago by revol_ufiaw
Define the $\text{\textcolor{red}{Pell Sequence}}$ as $$P_0=0,P_1=1,\;P_{n+2}=2P_{n+1}+P_n.$$Prove that $4P_{2k}^2+1$ is prime for all $k\in\mathbb N.$
1 reply
Entrepreneur
4 hours ago
revol_ufiaw
an hour ago
J
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Unknown triangle area
smartvong   1
N 2 hours ago by smartvong
The diagram shows a convex quadrilateral $ABCD$. The points $E$ and $F$ divide $AB$ into three equal parts while the points $G$ and $H$ divide $CD$ into three equal parts. The line segments $AH$ and $ED$ intersect at $I$. The line segments $CF$ and $BG$ intersect at $J$. Given that the areas of the triangles $AID$, $EHI$ and $FJG$ are $154$, $112$, and $99$ respectively, find the area of the triangle $BJC$.

IMAGE
1 reply
smartvong
May 8, 2025
smartvong
2 hours ago
J
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Geometry
AlexCenteno2007   4
N 2 hours ago by Raul_S_Baz
Let ABC be an acute triangle and let D, E and F be the feet of the altitudes from A, B and C respectively. The straight line EF and the circumcircle of ABC intersect at P such that F is between E and P, the straight lines BP and DF intersect at Q. Show that if ED = EP then CQ and DP are parallel.
4 replies
AlexCenteno2007
Apr 28, 2025
Raul_S_Baz
2 hours ago
J
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Inequalities
sqing   1
N 2 hours ago by sqing
Let $ 0\leq x,y,z\leq 2. $ Prove that
$$-48\leq (x-yz)( 3y-zx)(z-xy)\leq 9$$$$-144\leq (3x-yz)(y-zx)(3z-xy)\leq\frac{81}{64}$$$$-144\leq (3x-yz)(2y-zx)(3z-xy)\leq\frac{81}{16}$$
1 reply
sqing
Yesterday at 8:50 AM
sqing
2 hours ago
J
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Calculate the distance AD
MTA_2024   2
N 3 hours ago by WheatNeat
A semi-circle is inscribed in a quadrilateral $ABCD$. The center $O$ of the semi-circle is the midpoint of segment $AD$. We have $AB=9$ and $CD=16$.
Calculate the distance $AD$.
2 replies
MTA_2024
Yesterday at 3:50 PM
WheatNeat
3 hours ago
J
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Concurrent in a pyramid
vanstraelen   0
Today at 7:13 AM

Given a pyramid $(T,ABCD)$ where $ABCD$ is a parallelogram.
The intersection of the diagonals of the base is point $S$.
Point $A$ is connected to the midpoint of $[CT]$, point $B$ to the midpoint of $[DT]$,
point $C$ to the midpoint of $[AT]$ and point $D$ to the midpoint of $[BT]$.
a) Prove: the four lines are concurrent in a point $P$.
b) Calulate $\frac{TS}{TP}$.
0 replies
vanstraelen
Today at 7:13 AM
0 replies
J
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A problem with a rectangle
Raul_S_Baz   16
N Today at 7:09 AM by Raul_S_Baz
On the sides AB and AD of the rectangle ABCD, points M and N are taken such that MB = ND. Let P be the intersection of BN and CD, and Q be the intersection of DM and CB. How can we prove that PQ || MN?
IMAGE
16 replies
Raul_S_Baz
Apr 26, 2025
Raul_S_Baz
Today at 7:09 AM
J
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Number of real roots
girishpimoli   5
N Today at 6:21 AM by mrgenius000
If $f(x)=x^2-2x$. Then number of real roots of $f(f(f(f(x))))=3$
5 replies
girishpimoli
Today at 3:44 AM
mrgenius000
Today at 6:21 AM
J
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Proving that the line passes through the midpoint.
MTA_2024   2
N Today at 5:00 AM by Royal_mhyasd
Let $ABC$ be a triangle of orthocenter $H$. The circle of diameter $AC$ and the circumcircle of triangle $AHB$ intersect a second time in $K$.
Prove that the line $(CK)$ passes through the midpoint of segment $HB$.
2 replies
MTA_2024
May 7, 2025
Royal_mhyasd
Today at 5:00 AM
J
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Square number
linkxink0603   4
N Today at 3:29 AM by pooh123
Find m is positive interger such that m^4+3^m is square number
4 replies
linkxink0603
Yesterday at 11:20 AM
pooh123
Today at 3:29 AM
J
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J
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domino question
kjhgyuio   0
Apr 21, 2025
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0 replies
kjhgyuio
Apr 21, 2025
0 replies
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domino question
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62 posts
kjhgyuio
#1 h  Apr 21, 2025, 10:02 PM
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