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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]
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0 replies
jlacosta
May 1, 2025
0 replies
Logarithmic function
jonny   2
N 11 minutes ago by KSH31415
If $\log_{6}(15) = a$ and $\log_{12}(18)=b,$ Then $\log_{25}(24)$ in terms of $a$ and $b$
2 replies
jonny
Jul 15, 2016
KSH31415
11 minutes ago
book/resource recommendations
walterboro   0
2 hours ago
hi guys, does anyone have book recs (or other resources) for like aime+ level alg, nt, geo, comb? i want to learn a lot of theory in depth
also does anyone know how otis or woot is like from experience?
0 replies
walterboro
2 hours ago
0 replies
Engineers Induction FTW
RP3.1415   11
N 4 hours ago by Markas
Define a sequence as $a_1=x$ for some real number $x$ and \[ a_n=na_{n-1}+(n-1)(n!(n-1)!-1) \]for integers $n \geq 2$. Given that $a_{2021} =(2021!+1)^2 +2020!$, and given that $x=\dfrac{p}{q}$, where $p$ and $q$ are positive integers whose greatest common divisor is $1$, compute $p+q.$
11 replies
1 viewing
RP3.1415
Apr 26, 2021
Markas
4 hours ago
Incircle concurrency
niwobin   0
Today at 4:28 PM
Triangle ABC with incenter I, incircle is tangent to BC, AC, and AB at D, E and F respectively.
DT is a diameter for the incircle, and AT meets the incircle again at point H.
Let DH and EF intersect at point J. Prove: AJ//BC.
0 replies
niwobin
Today at 4:28 PM
0 replies
Weird locus problem
Sedro   1
N Today at 4:20 PM by sami1618
Points $A$ and $B$ are in the coordinate plane such that $AB=2$. Let $\mathcal{H}$ denote the locus of all points $P$ in the coordinate plane satisfying $PA\cdot PB=2$, and let $M$ be the midpoint of $AB$. Points $X$ and $Y$ are on $\mathcal{H}$ such that $\angle XMY = 45^\circ$ and $MX\cdot MY=\sqrt{2}$. The value of $MX^4 + MY^4$ can be expressed in the form $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
1 reply
Sedro
Today at 3:12 AM
sami1618
Today at 4:20 PM
Inequalities
sqing   4
N Today at 3:35 PM by sqing
Let $ a,b,c\geq 0 , (a+8)(b+c)=9.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq  \frac{38}{23}$$Let $ a,b,c\geq 0 , (a+2)(b+c)=3.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq  \frac{2(2\sqrt{3}+1)}{5}$$
4 replies
sqing
Yesterday at 12:50 PM
sqing
Today at 3:35 PM
Find the range of 'f'
agirlhasnoname   1
N Today at 2:46 PM by Mathzeus1024
Consider the triangle with vertices (1,2), (-5,-1) and (3,-2). Let Δ denote the region enclosed by the above triangle. Consider the function f:Δ-->R defined by f(x,y)= |10x - 3y|. Then the range of f is in the interval:
A)[0,36]
B)[0,47]
C)[4,47]
D)36,47]
1 reply
agirlhasnoname
May 14, 2021
Mathzeus1024
Today at 2:46 PM
Function equation
hoangdinhnhatlqdqt   1
N Today at 1:52 PM by Mathzeus1024
Find all functions $f:\mathbb{R}\geq 0\rightarrow \mathbb{R}\geq 0$ satisfying:
$f(f(x)-x)=2x\forall x\geq 0$
1 reply
hoangdinhnhatlqdqt
Dec 17, 2017
Mathzeus1024
Today at 1:52 PM
Inequality with function.
vickyricky   3
N Today at 1:51 PM by SpeedCuber7
If x satisfies the inequalit$ |x - 1| + |x - 2| + |x - 3| \ge 6$, then
$(a) 0 \le x \le 4. (b) x \le 0 or x \ge 4. (c) x \le -2 or x \ge 4$. (d) None of these.
3 replies
vickyricky
May 28, 2018
SpeedCuber7
Today at 1:51 PM
Writing/Evaluating Exponential Functions
Samarthsshah   1
N Today at 1:47 PM by Mathzeus1024
Rewrite the function and determine if the function represents exponential growth or decay. Identify the percent rate of change.

y=2(9)^-x/2
1 reply
Samarthsshah
Jan 30, 2018
Mathzeus1024
Today at 1:47 PM
Functional equation
TuZo   1
N Today at 1:37 PM by Mathzeus1024
My question is, if we can determinate or not, all $f:R\to R$ continuous function with $sin(f(x+y))=sin(f(x)+f(y))$ for all real $x,y$.
Thank you!
1 reply
TuZo
Oct 23, 2018
Mathzeus1024
Today at 1:37 PM
Real parameter equation
L.Lawliet03   1
N Today at 1:12 PM by Mathzeus1024
For which values of the real parameter $a$ does only one solution to the equation $(a+1)x^{2} -(a^{2} + a + 6)x +6a = 0$ belong to the interval (0,1)?
1 reply
L.Lawliet03
Nov 3, 2019
Mathzeus1024
Today at 1:12 PM
a inequality problem
Polus425   1
N Today at 12:36 PM by Mathzeus1024
$x_1,x_2\; are\; such\; two\; different\; real\; numbers:\; $
$(x_1 ^2 -2x_1 +4ln\, x_1)+(x_2 ^2 -2x_2 +4ln\, x_2)- x_1 ^2 x_2 ^2=0$
$prove\; that:\; x_1+x_2\ge 3$
1 reply
Polus425
Dec 19, 2019
Mathzeus1024
Today at 12:36 PM
Function of Common Area [China HS Mathematics League 2021]
HamstPan38825   1
N Today at 11:35 AM by Mathzeus1024
Define the regions $M, N$ in the Cartesian Plane as follows:
\begin{align*}
M &= \{(x, y) \in \mathbb R^2 \mid 0 \leq y \leq \text{min}(2x, 3-x)\} \\
N &= \{(x, y) \in \mathbb R^2 \mid t \leq x \leq t+2 \}
\end{align*}for some real number $t$. Denote the common area of $M$ and $N$ for some $t$ be $f(t)$. Compute the algebraic form of the function $f(t)$ for $0 \leq t \leq 1$.

(Source: China National High School Mathematics League 2021, Zhejiang Province, Problem 5)
1 reply
HamstPan38825
Jun 29, 2021
Mathzeus1024
Today at 11:35 AM
Vieta's Bash (I think??)
Sid-darth-vater   8
N Apr 21, 2025 by Sid-darth-vater
I technically have a solution (I didn't come up with it, it was the official solution) but it seems unintuitive. Can someone find a sol/explain to me how they got to it? (like why did u do the steps that u did) sorry if this seems a lil vague

8 replies
Sid-darth-vater
Apr 21, 2025
Sid-darth-vater
Apr 21, 2025
Vieta's Bash (I think??)
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Sid-darth-vater
42 posts
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I technically have a solution (I didn't come up with it, it was the official solution) but it seems unintuitive. Can someone find a sol/explain to me how they got to it? (like why did u do the steps that u did) sorry if this seems a lil vague
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StrahdVonZarovich
2138 posts
#2
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image caption:
let $a,~b,$ and $c$ be real numbers sach that $abc=-1,~a+b+c=4,$ and $\frac{a}{a^2-3a-1}+\frac{b}{b^2-3b-1}+\frac{c}{c^2-3c-1}=\frac{4}{9}.$ if $a^2+^2+c^2=\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers, what is $m+n?$
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MathBot101101
17 posts
#3
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What's the official solution? (i dunno which solution you don't want :sob:)
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ReticulatedPython
684 posts
#4
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Is it an alcumus problem?
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StrahdVonZarovich
2138 posts
#5
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yeah, is there a source to this?
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imagien_bad
58 posts
#6 • 1 Y
Y by Sid-darth-vater
North Carolina State Mathematics Contest 2024 Integer-Answer Problem 3
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StrahdVonZarovich
2138 posts
#7
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my inclination, having $abc$ and $a+b+c$ defined, and with another symmetric equation in $abc,$ would be to attempt to write the third equation in terms of the symmetric sums of $a,b,c,$ then substitute the first and third sums so we can find the second, its then pretty trivial to find $a^2+b^2+c^2$
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vanstraelen
9026 posts
#8 • 1 Y
Y by Sid-darth-vater
https://math.stackexchange.com/questions/4950163/if-abc-4-abc-1-fracaa2-3a-1-fracbb2-3b-1-fraccc2-3c-1
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Sid-darth-vater
42 posts
#9
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thank you @vanstraelen! the polynomial long division methods rlly clever!

bro, i forgot that I can still google questions :sob: im so used to thinking nothing will pop up that I posted on forums before thinking about google
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