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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.

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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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an exponential inequality with two variables
teresafang   0
9 minutes ago
x and y are positive real numbers.prove that [(x^y)/y]^(1/2)+[(y^x)/x]^(1/2)>=2.
sorry.I’m not good at English.Also I don’t know how to use Letax.
0 replies
teresafang
9 minutes ago
0 replies
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Arbitrary point on BC and its relation with orthocenter
falantrng   31
N 18 minutes ago by NZP_IMOCOMP4
Source: Balkan MO 2025 P2
In an acute-angled triangle \(ABC\), \(H\) be the orthocenter of it and \(D\) be any point on the side \(BC\). The points \(E, F\) are on the segments \(AB, AC\), respectively, such that the points \(A, B, D, F\) and \(A, C, D, E\) are cyclic. The segments \(BF\) and \(CE\) intersect at \(P.\) \(L\) is a point on \(HA\) such that \(LC\) is tangent to the circumcircle of triangle \(PBC\) at \(C.\) \(BH\) and \(CP\) intersect at \(X\). Prove that the points \(D, X, \) and \(L\) lie on the same line.

Proposed by Theoklitos Parayiou, Cyprus
31 replies
falantrng
Apr 27, 2025
NZP_IMOCOMP4
18 minutes ago
J
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IMO Genre Predictions
ohiorizzler1434   23
N 24 minutes ago by ohiorizzler1434
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
23 replies
ohiorizzler1434
Yesterday at 6:51 AM
ohiorizzler1434
24 minutes ago
J
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Number theory
gggzul   0
33 minutes ago
Is the number
$$10^{32}+10^{28}+...+10^4+1$$a perfect square?
0 replies
gggzul
33 minutes ago
0 replies
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1 line solution to Inequality
ItzsleepyXD   2
N Apr 30, 2025 by Vivaandax
Source: Own , Mock Thailand Mathematic Olympiad P8
Let $x_1,x_2,\dots,x_n$ be positive real number such that $x_1^2+x_2^2+\cdots+x_n^2=2$ Prove that
$$\sum_{i=1}^{n}\frac{1}{x_i^3(x_{i-1}+x_{i+1})}\geqslant \left(\sum_{i=1}^{n}\frac{x_i}{x_{i-1}+x_{i+1}}\right)^3$$such that $x_{n+1}=x_1$ and $x_0=x_n$
2 replies
ItzsleepyXD
Apr 30, 2025
Vivaandax
Apr 30, 2025
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1 line solution to Inequality
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inequalities
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Source: Own , Mock Thailand Mathematic Olympiad P8
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ItzsleepyXD
130 posts
ItzsleepyXD
#1 h  Apr 30, 2025, 9:27 AM
Y by
Let $x_1,x_2,\dots,x_n$ be positive real number such that $x_1^2+x_2^2+\cdots+x_n^2=2$ Prove that
$$\sum_{i=1}^{n}\frac{1}{x_i^3(x_{i-1}+x_{i+1})}\geqslant \left(\sum_{i=1}^{n}\frac{x_i}{x_{i-1}+x_{i+1}}\right)^3$$such that $x_{n+1}=x_1$ and $x_0=x_n$
This post has been edited 1 time. Last edited by ItzsleepyXD, May 1, 2025, 1:33 AM
Reason: Positive integer to positive real
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mihaig
7360 posts
mihaig
#2 h  Apr 30, 2025, 1:56 PM
Y by
Difficult, of course. Who is the author?
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Vivaandax
81 posts
Vivaandax
#3 h  Apr 30, 2025, 7:51 PM
Y by
If all the x_i are positive real integers, then x_i can only equal one right???
Did you mean to write positive reals instead of positive integers?
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ItzsleepyXD
130 posts
ItzsleepyXD
#4 h  May 1, 2025, 1:34 AM
Y by
Vivaandax wrote:
If all the x_i are positive real integers, then x_i can only equal one right???
Did you mean to write positive reals instead of positive integers?
thanks ,I edited
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