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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.

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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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Inequalities
sqing   3
N 16 minutes ago by DAVROS
Let $ a,b>0, a^2+ab+b^2 \geq 6 $. Prove that
$$a^4+ab+b^4\geq 10$$Let $ a,b>0, a^2+ab+b^2 \leq \sqrt{10} $. Prove that
$$a^4+ab+b^4 \leq 10$$Let $ a,b>0, a^2+ab+b^2 \geq \frac{15}{2} $. Prove that
$$ a^4-ab+b^4\geq 10$$Let $ a,b>0, a^2+ab+b^2 \leq \sqrt{10} $. Prove that
$$-\frac{1}{8}\leq a^4-ab+b^4\leq 10$$
3 replies
sqing
Yesterday at 2:42 PM
DAVROS
16 minutes ago
J
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Inequalities
sqing   0
an hour ago
Let $ 0\leq x,y,z\leq 2. $ Prove that
$$-48\leq (x-yz)( 3y-zx)(z-xy)\leq 9$$$$-144\leq (3x-yz)(y-zx)(3z-xy)\leq\frac{81}{64}$$$$-144\leq (3x-yz)(2y-zx)(3z-xy)\leq\frac{81}{16}$$
0 replies
sqing
an hour ago
0 replies
J
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How inflated are current aime/amc problems
derekli   2
N 3 hours ago by Mathgloggers
So I've been working on a math grinding tool in Stellar Learning (https://stellarlearning.app/competitive) and I was wondering how to make an algorithm that can calculate the difficulty of a problem. Specifically I want to know how difficult past AIMEs and AMC 10s and other contests are, compared to our current contests. I'm planning to make a problem ELO system similar to mathdash or something like that. Any help would be appreciated! Again if you would like to support me you may consider joining our developer team! :D
2 replies
derekli
Today at 1:30 AM
Mathgloggers
3 hours ago
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2023 Official Mock NAIME #15 f(f(f(x))) = f(f(x))
parmenides51   1
N 5 hours ago by jasperE3
How many non-bijective functions $f$ exist that satisfy $f(f(f(x))) = f(f(x))$ for all real $x$ and the domain of f is strictly within the set of $\{1,2,3,5,6,7,9\}$, the range being $\{1,2,4,6,7,8,9\}$?

Even though this is an AIME problem, a proof is mandatory for full credit. Constants must be ignored as we dont want an infinite number of solutions.
1 reply
parmenides51
Dec 4, 2023
jasperE3
5 hours ago
J
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Inequalities
sqing   3
N Today at 3:29 AM by sqing
Let $ a,b>0 $ and $\frac{a}{a^2+3}+ \frac{b}{b^2+ 3} \geq \frac{1}{2} . $ Prove that
$$a^2+ab+b^2\geq 3$$$$a^2-ab+b^2 \geq 1 $$Let $ a,b>0 $ and $\frac{a}{a^3+3}+ \frac{b}{b^3+ 3}\geq \frac{1}{2} . $ Prove that
$$a^3+ab+b^3 \geq 3$$$$ a^3-ab+b^3\geq 1 $$
3 replies
sqing
Wednesday at 12:59 PM
sqing
Today at 3:29 AM
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exist solutions?
teomihai   6
N Today at 12:05 AM by iwastedmyusername
Find how many perfect squares of five different digits there are, with elements from the set ${0,1,4,6,9}$.
6 replies
teomihai
Yesterday at 5:04 PM
iwastedmyusername
Today at 12:05 AM
J
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A pentagon inscribed in a circle of radius √2
tom-nowy   6
N Yesterday at 11:55 PM by anticodon
Can a pentagon with all rational side lengths be inscribed in a circle of radius $\sqrt{2}$ ?
6 replies
tom-nowy
May 6, 2025
anticodon
Yesterday at 11:55 PM
J
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Menelau's theorem
noneofyou34   6
N Yesterday at 11:10 PM by Shan3t
Please can someone help me prove that orthocenter of a triangle exists by using Menelau's Theorem!
6 replies
noneofyou34
Yesterday at 5:52 PM
Shan3t
Yesterday at 11:10 PM
J
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a,b,c irrational, f(x)=ax^2+bx+c : [-1,1] to [-1,1] surjective
tom-nowy   0
Yesterday at 11:03 PM
Consider a quadratic function $f(x) = ax^2 + bx + c$, where the coefficients $a, b,$ and $c$ are all irrational numbers.
Is it possible for this function to have a maximum value of $1$ and a minimum value of $-1$ over the interval $[-1, 1]$?
0 replies
tom-nowy
Yesterday at 11:03 PM
0 replies
J
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Math analytical geometry
JDog22   2
N Yesterday at 8:37 PM by Alex-131
Could you please tell me if this is correct:
If you take the position vector of an arbitrary point P, which is known to lie on the plane E, then the dot product of P and the normal vector n always results in the same number, regardless of the coordinates of point P. As long as the point lies on the plane, this calculation always gives the same number. Is that true?
2 replies
JDog22
Yesterday at 8:24 PM
Alex-131
Yesterday at 8:37 PM
J
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Hard Inequality
William_Mai   14
N Yesterday at 5:34 PM by hi2024IMOp14
Given $a, b, c \in \mathbb{R}$ such that $a^2 + b^2 + c^2 = 1$.
Find the minimum value of $P = ab + 2bc + 3ca$.

Source: Pham Le Van
14 replies
William_Mai
May 3, 2025
hi2024IMOp14
Yesterday at 5:34 PM
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Geometry
MTA_2024   7
N Yesterday at 4:56 PM by hi2024IMOp14
Let $ABC$ be a triangle such that $AB=3$,$BC=5$ and $AC=6$.Let $D$ be a point on side $AC$ and $E$ one on side $BC$ so that the line $DE$ is tangent to the incircle of $\triangle ABC$ .
Evaluate the perimeter of triangle $\triangle CDE$.
7 replies
MTA_2024
Wednesday at 6:52 PM
hi2024IMOp14
Yesterday at 4:56 PM
J
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four point lie on circle
Kizaruno   0
Yesterday at 3:29 PM
Let triangle ABC be inscribed in a circle with center O. A line d intersects sides AB and AC at points E and D, respectively. Let M, N, and P be the midpoints of segments BD, CE, and DE, respectively. Let Q be the foot of the perpendicular from O to line DE. Prove that the points M, N, P, and Q lie on a circle.
0 replies
Kizaruno
Yesterday at 3:29 PM
0 replies
J
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Range if \omega for No Inscribed Right Triangle y = \sin(\omega x)
ThisIsJoe   0
Yesterday at 2:02 PM
For a positive number \omega , determine the range of \omega for which the curve y = \sin(\omega x) has no inscribed right triangle.
Could someone help me figure out how to approach this?
0 replies
ThisIsJoe
Yesterday at 2:02 PM
0 replies
J
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J
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Any tips for IOQM(indian olympiad qualifier for math)
Indianmathenthusiast1234   4
N Apr 17, 2025 by Indianmathenthusiast1234
Guys I'm preparing for the IOQM, and i feel like the linear congruences, modular arithmetic and number bases are a bit hard to grasp. Any tips?
4 replies
Indianmathenthusiast1234
Apr 17, 2025
Indianmathenthusiast1234
Apr 17, 2025
J
Any tips for IOQM(indian olympiad qualifier for math)
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Reveal topic tags
Competition Math
modular arithmetic
Bases
number theory
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Indianmathenthusiast1234
8 posts
Indianmathenthusiast1234
#1 h  Apr 17, 2025, 3:49 PM
Y by
Guys I'm preparing for the IOQM, and i feel like the linear congruences, modular arithmetic and number bases are a bit hard to grasp. Any tips?
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Alex-131
5388 posts
Alex-131
#2 h  Apr 17, 2025, 3:51 PM
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intro to number theory
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Indianmathenthusiast1234
8 posts
Indianmathenthusiast1234
#3 h  Apr 17, 2025, 3:53 PM
Y by
Done with that book. Any general ones?
Btw thanks for the advice :)
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Alex-131
5388 posts
Alex-131
#4 h  Apr 17, 2025, 3:55 PM
Y by
You can take a look at MONT (modern olympiad number theory), maybe the first two chapters. It's structured for more olympiads, but may be helpful if you've done intro to nt before.

You could also mess around with OTIS Excerpts, specifically the nt part.
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Indianmathenthusiast1234
8 posts
Indianmathenthusiast1234
#5 h  Apr 17, 2025, 4:08 PM
Y by
Thank you so much
I will definitely look into it
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