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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Jun 2, 2025
0 replies
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inequality
luckvoltia.112   0
3 hours ago
$ \text{Let } a, b, c \text{ be non-negative real numbers such that } ab + bc + ca = 1. \text{ Prove that } \frac{(1 + a^2)^2}{b^2 + c^2} + \frac{(1 + b^2)^2}{c^2 + a^2} + \frac{(1 + c^2)^2}{a^2 + b^2} \geq 8. $
0 replies
luckvoltia.112
3 hours ago
0 replies
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Quadratic Equation
EntangledElectron99   0
4 hours ago
If $\alpha \ and \ \beta$ are roots of $ x^2 - 6x +2 = 0$ and $ S(n_1,n_2) = 3\alpha^{n_1} + 5\beta^{n_2} $ for
$ n_1 , n_2 \ge 2 $, then which of the following is true?[Multiple options maybe correct]

a) $ S(100,99) - 6S(99,98) + 2S(98,97) = 0 $
b)$ S(10,11) - 6S(9,10) + 2S(8,9) = 0 $
c) $ S(99,100) - 6S(98,99) + 2S(97,98) = 0 $
d) $ S(11,10) - 6S(10,9) + 2S(9,8) = 0 $

0 replies
EntangledElectron99
4 hours ago
0 replies
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[Sipnayan SHS 2025] Semifinals Round, Average, #7:
LilKirb   1
N 4 hours ago by Viliciri
Let $n$ be a randomly chosen divisor of $30^6.$ Find the probability that $2n$ has more positive divisors than both $3n$ and $5n.$
1 reply
LilKirb
4 hours ago
Viliciri
4 hours ago
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Inequalities
sqing   16
N 4 hours ago by sqing
Let $ a,b> 0 ,\frac{a}{2b+1}+\frac{b}{3}+\frac{1}{2a+1} \leq 1.$ Prove that
$$ a^2+b^2 -ab\leq 1$$$$ a^2+b^2 +ab \leq3$$Let $ a,b,c> 0 , \frac{a}{2b+1}+\frac{b}{2c+1}+\frac{c}{2a+1} \leq 1.$ Prove that
$$ a +b +c +abc \leq 4$$
16 replies
sqing
May 24, 2025
sqing
4 hours ago
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[12th PMO Qualifying Stage for Regions 1, 2, and CAR: II.19]
reilynso   1
N 4 hours ago by reilynso
Three of the roots of the equation 2x^4 + ax^2 + bx + c = 0 are -1, 2, and -3. What is b?

a) 0 b) 6 c) 8 d) -18
1 reply
reilynso
4 hours ago
reilynso
4 hours ago
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[23rd PMO Qualifying Stage: I.5]
reilynso   1
N 4 hours ago by reilynso
Find the sum of all k for which x^5 + kx^4 - 6x^3 - 15x^2 - 8k^3x - 12k + 21 leaves a remainder of 23 when divided by 0.

(a) -1 (b) -3/4 (c) 5/8 (d) 3/4
1 reply
reilynso
4 hours ago
reilynso
4 hours ago
J
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inequality
luckvoltia.112   4
N 4 hours ago by sqing
Given that $a, b, c$ are non-negative real numbers such that $a + b + c = 3$. Find the maximum value of

$$ P = \sqrt{(a^2 + 3)(b^2 + 3)} + \sqrt{(b^2 + 3)(c^2 + 3)} + \sqrt{(c^2 + 3)(a^2 + 3)}. $$
4 replies
luckvoltia.112
Yesterday at 3:11 PM
sqing
4 hours ago
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Bounding With Powers
Shreyasharma   6
N 5 hours ago by jacosheebay
Is this a valid solution for the following problem (St. Petersburg 1996):

Find all positive integers $n$ such that,

$$ 3^{n-1} + 5^{n-1} | 3^n + 5^n$$
Solution
6 replies
Shreyasharma
Jul 11, 2023
jacosheebay
5 hours ago
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Difficult Triangle Angle Chasing
Viliciri   2
N 5 hours ago by Viliciri
In $\triangle{ABC}$, $\angle{ABC} = 54^{\circ}$ and $\angle{ACB} = 24^{\circ}$.
If $D$ lies on segment $BC$ such that $AC=BD$, what is the measure of $\angle{DAC}$?

Credit to Nathan Liu for communicating this problem to me.
2 replies
Viliciri
Today at 3:12 AM
Viliciri
5 hours ago
J
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Inequalities
sqing   5
N Today at 11:43 AM by sqing
Let $ a,b,c\geq 0,a+b+c=1. $ Prove that
$$ 7\geq \frac{2+a}{2-a}+\frac{3+2b}{3 -2b}+\frac{2+c}{2 -c}\geq \frac{11+16\sqrt {3}}{9}$$$$5\geq \frac{2+a}{2-a}+\frac{5+2b}{5 -2b}+\frac{2+c}{2 -c}\geq \frac{9+16\sqrt {5}}{11}$$$$5\geq \frac{2+a}{2-a}+\frac{7+2b}{7 -2b}+\frac{2+c}{2 -c}\geq \frac{7+16\sqrt{7}}{13}$$
5 replies
sqing
Jun 13, 2025
sqing
Today at 11:43 AM
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Filter by unsolved
Suntafayato   1
N Yesterday at 3:28 AM by aidan0626
Lots of posts have many good solutions.

How to filter posts that have never been solved by anyone? A sufficient condition: posts with zero replies.
1 reply
Suntafayato
Yesterday at 3:23 AM
aidan0626
Yesterday at 3:28 AM
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k error in contest collection
heheman   2
N Friday at 10:54 PM by jlacosta
hello friends,
in the 2023 Iran MO 3rd round contest collection, the geometry section has been mistakenly titled as Algebra. Can someone fix?
Link:
https://artofproblemsolving.com/community/c3509728_2023_iran_mo_3rd_round
Screenshot provided as attachment
2 replies
heheman
Jun 18, 2025
jlacosta
Friday at 10:54 PM
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k Long time to load
SI113   1
N Friday at 10:29 PM by jlacosta
Not a complaint or anything, since it only takes max a minute, but is there any particular reason the AoPS wiki takes a while to load compared to other parts of the website?
1 reply
SI113
Friday at 10:27 PM
jlacosta
Friday at 10:29 PM
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k Absolute Value
Yash1212   1
N Jun 20, 2025 by Demetri
Does anybody know how to write the absolute value symbol in AoPS
1 reply
Yash1212
Jun 20, 2025
Demetri
Jun 20, 2025
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k Alcumus bug
MathLoverYeah   1
N Jun 12, 2025 by ibmo0907
URL: aops.com/alcumus
I was working on the Mixed Numbers section of Alcumus. After I solved a problem, it showed XP being gained in precalculus for some reason. Why is this?
Steps to reproduce:
1. Finish a problem in Mixed Numbers and level up in something
Expected behavior: No precalculus Xp gain
Frequency: Not sure
Operating system(s): Windows 11
Browser(s), including version: Microsoft Edge 132
Additional information: None
1 reply
MathLoverYeah
Jun 12, 2025
ibmo0907
Jun 12, 2025
J
Alcumus bug
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Reveal topic tags
Alcumus
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G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
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MathLoverYeah
111 posts
MathLoverYeah
#1 h  Jun 12, 2025, 8:47 PM
Y by
URL: aops.com/alcumus
I was working on the Mixed Numbers section of Alcumus. After I solved a problem, it showed XP being gained in precalculus for some reason. Why is this?
Steps to reproduce:
1. Finish a problem in Mixed Numbers and level up in something
Expected behavior: No precalculus Xp gain
Frequency: Not sure
Operating system(s): Windows 11
Browser(s), including version: Microsoft Edge 132
Additional information: None
Attachments:
This post has been edited 2 times. Last edited by MathLoverYeah, Jun 12, 2025, 8:49 PM
Reason: additional info
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ibmo0907
1201 posts
ibmo0907
#2 h  Jun 12, 2025, 8:51 PM
Y by
Whenever you complete a quest or achievement, you gain the amount of XP the quest/achievement gives (in your case, 75 XP) for all your subject levels.
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