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Infinite product problem
ReticulatedPython   6
N an hour ago by ReticulatedPython
Compute $$\prod_{n=1}^{\infty}3^{\frac{1}{2^{n-1}}}+1$$
hint

The solution to this problem is pretty short once you find out the trick. :D
6 replies
ReticulatedPython
2 hours ago
ReticulatedPython
an hour ago
Function equation
LeDuonggg   6
N an hour ago by MathLuis
Find all functions $f: \mathbb{R^+} \rightarrow \mathbb{R^+}$ , such that for all $x,y>0$:
\[ f(x+f(y))=\dfrac{f(x)}{1+f(xy)}\]
6 replies
LeDuonggg
Yesterday at 2:59 PM
MathLuis
an hour ago
Math and AI 4 Girls
mkwhe   37
N an hour ago by deeptisidana
Hey everyone!

The 2025 MA4G competition is now open!

Apply Here: https://xmathandai4girls.submittable.com/submit


Visit https://www.mathandai4girls.org/ to get started!

Feel free to PM or email mathandai4girls@yahoo.com if you have any questions!
37 replies
mkwhe
Apr 5, 2025
deeptisidana
an hour ago
What's the chance that two AoPS accounts generate with the same icon?
Math-lover1   0
2 hours ago
So I've been wondering how many possible "icons" can be generated when you first create an account. By "icon" I mean the stack of cubes as the first profile picture before changing it.

I don't know a lot about how AoPS icons generate, so I have a few questions:
- Do the colors on AoPS icons generate through a preset of colors or the RGB (red, green, blue in hexadecimal form) scale? If it generates through the RGB scale, then there may be greater than $256^3 = 16777216$ different icons.
- Do the arrangements of the stacks of blocks in the icon change with each account? If so, I think we can calculate this through considering each stack of blocks independently.
0 replies
Math-lover1
2 hours ago
0 replies
9 Have you participated in the MATHCOUNTS competition?
aadimathgenius9   29
N 3 hours ago by hashbrown2009
Have you participated in the MATHCOUNTS competition before?
29 replies
aadimathgenius9
Jan 1, 2025
hashbrown2009
3 hours ago
9 What is the most important topic in maths competition?
AVIKRIS   67
N Today at 2:31 PM by Craftybutterfly
I think arithmetic is the most the most important topic in math competitions.
67 replies
AVIKRIS
Apr 19, 2025
Craftybutterfly
Today at 2:31 PM
9 AMC 8 Scores
ChromeRaptor777   125
N Today at 2:12 PM by Soupboy0
As far as I'm certain, I think all AMC8 scores are already out. Vote above.
125 replies
ChromeRaptor777
Apr 1, 2022
Soupboy0
Today at 2:12 PM
Facts About 2025!
Existing_Human1   257
N Today at 1:49 PM by Charizard_637
Hello AOPS,

As we enter the New Year, the most exciting part is figuring out the mathematical connections to the number we have now temporally entered

Here are some facts about 2025:
$$2025 = 45^2 = (20+25)(20+25)$$$$2025 = 1^3 + 2^3 +3^3 + 4^3 +5^3 +6^3 + 7^3 +8^3 +9^3 = (1+2+3+4+5+6+7+8+9)^2 = {10 \choose 2}^2$$
If anyone has any more facts about 2025, enlighted the world with a new appreciation for the year


(I got some of the facts from this video)
257 replies
Existing_Human1
Jan 1, 2025
Charizard_637
Today at 1:49 PM
Berkeley mini Math Tournament Online is June 7
BerkeleyMathTournament   7
N Today at 1:39 PM by Inaaya
Berkeley mini Math Tournament is a math competition hosted for middle school students once a year. Students compete in multiple rounds: individual round, team round, puzzle round, and relay round.

BmMT 2025 Online will be held on June 7th, and registration is OPEN! Registration is $8 per student. Our website https://berkeley.mt/events/bmmt-2025-online/ has more details about the event, past tests to practice with, and frequently asked questions. We look forward to building community and inspiring students as they explore the world of math!

3 out of 4 of the rounds are completed with a team, so it’s a great opportunity for students to work together. Beyond getting more comfortable with math and becoming better problem solvers, our team is preparing some fun post-competition activities!

Registration is open to students in grades 8 or below. You do not have to be local to the Bay Area or California to register for BmMT Online. Students may register as a team of 1, but it is beneficial to compete on a team of at least 3 due to our scoring guideline and for the experience.

We hope you consider attending, or if you are a parent or teacher, that you encourage your students to think about attending BmMT. Thank you, and once again find more details/register at our website,https://berkeley.mt.
7 replies
BerkeleyMathTournament
Yesterday at 7:37 AM
Inaaya
Today at 1:39 PM
1234th Post!
PikaPika999   259
N Today at 12:14 PM by PikaPika999
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
259 replies
PikaPika999
Apr 21, 2025
PikaPika999
Today at 12:14 PM
9 What competitions do you do
VivaanKam   5
N Today at 4:45 AM by valisaxieamc

I know I missed a lot of other competitions so if you didi one of the just choose "Other".
5 replies
VivaanKam
Apr 30, 2025
valisaxieamc
Today at 4:45 AM
Continuity of function and line segment of integer length
egxa   2
N Apr 23, 2025 by NO_SQUARES
Source: All Russian 2025 11.8
Let \( f: \mathbb{R} \to \mathbb{R} \) be a continuous function. A chord is defined as a segment of integer length, parallel to the x-axis, whose endpoints lie on the graph of \( f \). It is known that the graph of \( f \) contains exactly \( N \) chords, one of which has length 2025. Find the minimum possible value of \( N \).
2 replies
egxa
Apr 18, 2025
NO_SQUARES
Apr 23, 2025
Continuity of function and line segment of integer length
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Source: All Russian 2025 11.8
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egxa
209 posts
#1
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Let \( f: \mathbb{R} \to \mathbb{R} \) be a continuous function. A chord is defined as a segment of integer length, parallel to the x-axis, whose endpoints lie on the graph of \( f \). It is known that the graph of \( f \) contains exactly \( N \) chords, one of which has length 2025. Find the minimum possible value of \( N \).
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tonykuncheng
21 posts
#2
Y by
is it $1$?
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NO_SQUARES
1093 posts
#3
Y by
tonykuncheng wrote:
is it $1$?

No, answer is such.
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