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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Inequality with a,b,c
GeoMorocco   7
N 10 minutes ago by math90
Source: Morocco Training 2025
Let $ a,b,c $ be positive real numbers such that : $ ab+bc+ca=3 $ . Prove that : $$\frac{a\sqrt{3+bc}}{b+c}+\frac{b\sqrt{3+ca}}{c+a}+\frac{c\sqrt{3+ab}}{a+b}\ge a+b+c $$
7 replies
GeoMorocco
Thursday at 9:51 PM
math90
10 minutes ago
J
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Combinatorics game
VicKmath7   3
N 20 minutes ago by Topiary
Source: First JBMO TST of France 2020, Problem 1
Players A and B play a game. They are given a box with $n=>1$ candies. A starts first. On a move, if in the box there are $k$ candies, the player chooses positive integer $l$ so that $l<=k$ and $(l, k) =1$, and eats $l$ candies from the box. The player who eats the last candy wins. Who has winning strategy, in terms of $n$.
3 replies
VicKmath7
Mar 4, 2020
Topiary
20 minutes ago
J
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Find all such primes
Entrepreneur   2
N 25 minutes ago by straight
Source: Own
Find all primes $p,q\;\&\;r$ such that $$\color{blue}{pq=r^2+r+1.}$$
2 replies
Entrepreneur
an hour ago
straight
25 minutes ago
J
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Inspired by giangtruong13
sqing   5
N 33 minutes ago by kokcio
Source: Own
Let $ a,b,c,d\geq 0 ,a-b+d=21 $ and $ a+3b+4c=101 $. Prove that
$$ 61\leq a+b+2c+d\leq \frac{265}{3}$$$$- \frac{2121}{2}\leq ab+bc-2cd+da\leq \frac{14045}{12}$$$$\frac{519506-7471\sqrt{7471}}{27}\leq ab+bc-2cd+3da\leq 33620$$
5 replies
sqing
Yesterday at 2:57 AM
kokcio
33 minutes ago
J
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Final epic for 2014
EpicSkills32   1
N Dec 2, 2016 by Kagebaka
$\ [\text{Blog Post 141}] $
Notes to self (to-do/stuff to blog about):
[list][*]Family camp (where I saw programming1157)
[*]Christmas vacation
[*]European dodgeball
[*]PSAT and SAT[/list]
well darn can't remember anything else. . .

But before I talk about that stuff, I'm gonna take the little time at the end of this year to talk about . . . this year.
Later I'll make some more in-depth observations and reflections, but for now I just need to get on here and share some long-overdue stuff, mostly music that I've found recently but still haven't shared.

$\dfrac{\text{Epic}}{\text{Item(s)}} 171-191 $

Electronic music!

Oh and I just have to say right now that Oliver Twist has, literally, the best plot of any story (film or book) ever. (Ok there are probably others that I've read/seen before, but I've read Oliver Twist twice now and both times after finishing it I've thought "dayum that was good.")

Well I guess that's it for tonight; it's almost 1:00 A.M. so yea. . . Goin bowling tomorrow with a bunch of guys from a sort-of church group.
I'll probably edit this post or make a new one with stuff I forgot, and, oh yeah, music from other genres XP
1 reply
EpicSkills32
Dec 30, 2014
Kagebaka
Dec 2, 2016
J
No more topics!
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EK= KU + UA ? <UKA =<KF E, <E=1/2 <U, angle bisector
parmenides51   0
Jan 5, 2021
Source: 2019 SPbU Qualifying round, grades 10-11 p5 - Saint Petersburg State University School Olympiad
In a convex quadrilateral $UEFA$, the angle $E$ is half the angle $U$, and on the side $UE$ a point $K$ is marked such that $FK$ is the bisector of angle $F$ and angle $UKA$ is equal to angle $KFE$. Is it true that $EK= KU + U A$?
0 replies
parmenides51
Jan 5, 2021
0 replies
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EK= KU + UA ? <UKA =<KF E, <E=1/2 <U, angle bisector
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Reveal topic tags
geometry
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equal angles
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Source: 2019 SPbU Qualifying round, grades 10-11 p5 - Saint Petersburg State University School Olympiad
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parmenides51
30630 posts
parmenides51
#1 h  Jan 5, 2021, 6:43 PM
Y by
In a convex quadrilateral $UEFA$, the angle $E$ is half the angle $U$, and on the side $UE$ a point $K$ is marked such that $FK$ is the bisector of angle $F$ and angle $UKA$ is equal to angle $KFE$. Is it true that $EK= KU + U A$?
This post has been edited 1 time. Last edited by parmenides51, Jan 5, 2021, 6:44 PM
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