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Interesting functional equation
IvanRogers1   8
N an hour ago by IvanRogers1
Find all functions $f:  \mathbb{R} \to  \mathbb{R}$ such that $f(x + y) + f(xy) + 1 = f(x) + f(y) + f(xy + 1) \forall x ,y \in \mathbb R$.
8 replies
IvanRogers1
Yesterday at 3:19 PM
IvanRogers1
an hour ago
Compilation of Seq and Series Problems
Saucepan_man02   0
5 hours ago
Could anyone post some problems/resources on Seq and Series (based on AIME/ARML level)?
0 replies
Saucepan_man02
5 hours ago
0 replies
k Multiple black things [RESOLVED]
Yiyj   8
N May 12, 2025 by Yiyj
Why is there like multiple black thingies as shown in the attachments? When I also clicked on other threads, the black thingies for all of them stayed. So weird…
8 replies
Yiyj
May 12, 2025
Yiyj
May 12, 2025
File uploads on aops
ohiorizzler1434   3
N May 12, 2025 by Craftybutterfly
What is the length of time a file uploaded to cdn.artofproblemsolving lasts before it is taken down?
3 replies
ohiorizzler1434
May 12, 2025
Craftybutterfly
May 12, 2025
k Happy mother’s day
Rice_Farmer   4
N May 12, 2025 by JohannIsBach
Happy Mother’s Day!
4 replies
Rice_Farmer
May 11, 2025
JohannIsBach
May 12, 2025
k happy mothers day!
JohannIsBach   5
N May 12, 2025 by JohannIsBach
hi! happy mothers day! hows it goin? happy mothers day!
5 replies
JohannIsBach
May 11, 2025
JohannIsBach
May 12, 2025
k (Another) Reaper bug
RedChameleon   3
N May 8, 2025 by jlacosta
Sbarrack updated the home page of reaper. Now when I want to click on current or upcoming games, when I click the buttons, they do not redirect me to the game.

I have not recorded footage because I'm lazy but I'm currently on a Chromebook and I'm using Chrome.
3 replies
RedChameleon
May 8, 2025
jlacosta
May 8, 2025
k Is it a error for reaper
tyrantfire4   5
N May 8, 2025 by k1glaucus
I was going to reap on reaper and it put me on a strange reaper page I figured out to to reap by using the url
https://artofproblemsolving.com/reaper/reaper?id=85and changing the 85 but it was so weird I kept the page
5 replies
tyrantfire4
May 8, 2025
k1glaucus
May 8, 2025
Reaper bug
ChessPanther   3
N May 8, 2025 by Craftybutterfly
In reaper game 96 it says it begins in 3 days but when you look at the upcoming games it says it starts on June 10th? I don't know which it starts on.
3 replies
ChessPanther
May 8, 2025
Craftybutterfly
May 8, 2025
k Latex problem
hakuj   2
N May 8, 2025 by k1glaucus
Why is Latex not allowed in the text?It is said that new user is not allowed to post an image.How could I post a math problem without Latex?
2 replies
hakuj
May 8, 2025
k1glaucus
May 8, 2025
k Any way to collapse these huge headers?
ComicallyUnfunny   3
N May 8, 2025 by k1glaucus
As you can see, literally 60% of screen space is consumed by headers (even with the banner announcement closed). Is there any way to actually use more screen space for the content?
3 replies
ComicallyUnfunny
May 8, 2025
k1glaucus
May 8, 2025
Python exit() module decriptions appear as "undefined"
SoaringHigh   16
N May 7, 2025 by LostInBali
Summary of the problem: When using exit() (or quit()) in the Python windows on AoPS the "Description" and "To fix" options show up as "undefined"
sample program
Page URL: N/A
Steps to reproduce:
1. Use the AoPS Python module to execute the exit() or quit() functions in a program. (try running the sample program)
Expected behavior: The "Description" and "To fix" sections give a description of SystemExit
Frequency: Always
Operating system(s): Windows 11 Home
Browser(s), including version: Microsoft Edge 130.0.2849.46
Additional information: N/A
16 replies
SoaringHigh
Oct 22, 2024
LostInBali
May 7, 2025
Algebraic Manipulation
Darealzolt   1
N Apr 30, 2025 by Soupboy0
Find the number of pairs of real numbers $a, b, c$ that satisfy the equation $a^4 + b^4 + c^4 + 1 = 4abc$.
1 reply
Darealzolt
Apr 30, 2025
Soupboy0
Apr 30, 2025
Algebraic Manipulation
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Darealzolt
7 posts
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Find the number of pairs of real numbers $a, b, c$ that satisfy the equation $a^4 + b^4 + c^4 + 1 = 4abc$.
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Soupboy0
423 posts
#2
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$(a, b, c) = (1, 1, 1), (-1, -1, 1)$ and permutations. Note that if $a, b, c > 0$, then $a^4+b^4+c^4+1 \ge 4abc$ by AM-GM, with equality at $a=b=c=1$, which is the only solution for $a, b, c > 0$. Also note that if $1$ or all of $a, b, c$ are negative, then there are no solutions by the Trivial inequality. Also note that when $2$ of $a, b, c$ are negative, then this case is symmetric to $a, b, c > 0$. Therefore, there are $4$ solutions
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