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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.

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0 replies
jlacosta
Apr 2, 2025
0 replies
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Inequalities
sqing   28
N an hour ago by sqing
Let $ a,b $ be reals such that $ a^2+ab+b^2 =3$ . Prove that
$$ \frac{4}{ 3}\geq \frac{1}{ a^2+5 }+ \frac{1}{ b^2+5 }+ab \geq -\frac{11}{4 }$$$$ \frac{13}{ 4}\geq \frac{1}{ a^2+5 }+ \frac{1}{ b^2+5 }+ab \geq -\frac{2}{3 }$$$$ \frac{3}{ 2}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }+ab \geq -\frac{17}{6 }$$$$ \frac{19}{ 6}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }-ab \geq -\frac{1}{2}$$Let $ a,b $ be reals such that $ a^2-ab+b^2 =1 $ . Prove that
$$ \frac{3}{ 2}\geq \frac{1}{ a^2+3 }+ \frac{1}{ b^2+3 }+ab \geq \frac{4}{15 }$$$$ \frac{14}{ 15}\geq \frac{1}{ a^2+3 }+ \frac{1}{ b^2+3 }-ab \geq -\frac{1}{2 }$$$$ \frac{3}{ 2}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }+ab \geq \frac{13}{42 }$$$$ \frac{41}{ 42}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }-ab \geq -\frac{1}{2 }$$
28 replies
sqing
Apr 16, 2025
sqing
an hour ago
J
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can anyone solve this
averageguy   8
N 3 hours ago by Bole
Hi guys,
For some reason I can't think of a simple way to solve this problem. Is there anyway you guys can think of without trig or if it does have trig something elegant. Answer is 106 btw.
8 replies
+1 w
averageguy
Dec 26, 2024
Bole
3 hours ago
J
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Middle School Math <3
peace09   13
N 4 hours ago by Kevin2010
If $f(0)=1$ and $f(n)=\tfrac{n!}{\text{lcm}(1,2,\dots,n)}$ for each positive integer $n$, what is the value of $\tfrac{f(1)}{f(0)}+\tfrac{f(2)}{f(1)}+\dots+\tfrac{f(50)}{f(49)}$?

If you enjoyed the above problem, check out the 2024 WMC Series!
13 replies
peace09
Mar 11, 2024
Kevin2010
4 hours ago
J
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Theory of Equations
P162008   2
N 5 hours ago by P162008
Let $a,b,c,d$ and $e\in [-2,2]$ such that $\sum_{cyc} a = 0, \sum_{cyc} a^3 = 0, \sum_{cyc} a^5 = 10.$ Find the value of $\sum_{cyc} a^2.$
2 replies
P162008
Yesterday at 11:27 AM
P162008
5 hours ago
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No more topics!
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idk12345678 Math Contest
idk12345678   25
N Apr 19, 2025 by vsarg
Welcome to the 1st idk12345678 Math Contest.
You have 4 hours. You do not have to prove your answers.
Post \signup username to sign up. Post your answers in a hide tag and I will tell you your score.*


The contest is attached to the post

Clarifications

*I mightve done them wrong feel free to ask about an answer
25 replies
idk12345678
Apr 10, 2025
vsarg
Apr 19, 2025
J
idk12345678 Math Contest
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Reveal topic tags
math contests
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idk12345678
381 posts
idk12345678
#1 h  Apr 10, 2025, 2:34 PM
Y by
Welcome to the 1st idk12345678 Math Contest.
You have 4 hours. You do not have to prove your answers.
Post \signup username to sign up. Post your answers in a hide tag and I will tell you your score.*


The contest is attached to the post

Clarifications

*I mightve done them wrong feel free to ask about an answer
Attachments:
contest.pdf (26kb)
This post has been edited 1 time. Last edited by idk12345678, Apr 19, 2025, 12:47 AM
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idk12345678
381 posts
idk12345678
#2 h  Apr 10, 2025, 10:43 PM
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Hints
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mathprodigy2011
318 posts
mathprodigy2011
#3 h  Apr 10, 2025, 10:46 PM
Y by
idk12345678 wrote:
Hints

are a,b,c, and d integers for p1
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martianrunner
180 posts
martianrunner
#4 h  Apr 10, 2025, 11:13 PM
Y by
i wouldnt think so (i didnt get integers)
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mathprodigy2011
318 posts
mathprodigy2011
#5 h  Apr 10, 2025, 11:14 PM
Y by
martianrunner wrote:
i wouldnt think so (i didnt get integers)

yea me neither thats why i was asking lol
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idk12345678
381 posts
idk12345678
#6 h  Apr 10, 2025, 11:21 PM
Y by
mathprodigy2011 wrote:
idk12345678 wrote:
Hints

are a,b,c, and d integers for p1

i got integers... dm me ur sol and ill fix it if not
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martianrunner
180 posts
martianrunner
#7 h  Apr 11, 2025, 1:17 AM
Y by
also 3 is sorta simple
like i solved it in like 3 minutes (without generating functions)
This post has been edited 1 time. Last edited by martianrunner, Apr 11, 2025, 4:30 AM
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mathprodigy2011
318 posts
mathprodigy2011
#8 h  Apr 11, 2025, 1:31 AM
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martianrunner wrote:
also 3 is hella simple like i solved it in like 3 minutes (without generating functions)

its easy to guess as well (because) Click to reveal hidden text
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idk12345678
381 posts
idk12345678
#9 h  Apr 11, 2025, 1:55 AM
Y by
ig yeah. Has anyone solved 6 yet? that problem was so fun to write
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mathprodigy2011
318 posts
mathprodigy2011
#11 h  Apr 11, 2025, 2:30 AM
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idk12345678 wrote:
ig yeah. Has anyone solved 6 yet? that problem was so fun to write

I like the questions, they are fun; trying to do calculations for p6 rn
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idk12345678
381 posts
idk12345678
#12 h  Apr 11, 2025, 2:35 AM
Y by
Thanks!!
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martianrunner
180 posts
martianrunner
#13 h  Apr 11, 2025, 4:29 AM
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by the way I may have given off the wrong vibe with my comment, I apologize

the questions are very well-written, I really enjoyed the test

good job :)
This post has been edited 1 time. Last edited by martianrunner, Apr 11, 2025, 4:34 AM
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martianrunner
180 posts
martianrunner
#14 h  Apr 11, 2025, 4:34 AM
Y by
I have a question

where do you get the inspiration to create problems (like the ones in your test)

I also want to write problems but it takes a while and I wanted to know if you do something to help with that
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idk12345678
381 posts
idk12345678
#15 h  Apr 11, 2025, 4:36 AM
Y by
martianrunner wrote:
by the way I may have given off the wrong vibe with my comment, I apologize

the questions are very well-written, I really enjoyed the test

good job :)

thanks. you can dm me your answers and i can grade them if you want, and then u can be on the leaderboard
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idk12345678
381 posts
idk12345678
#16 h  Apr 11, 2025, 4:38 AM
Y by
martianrunner wrote:
I have a question

where do you get the inspiration to create problems (like the ones in your test)

I also want to write problems but it takes a while and I wanted to know if you do something to help with that

i started writing in spanish class yesterday cuz i was bored. i came up with ideas and then i made problems based on them
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martianrunner
180 posts
martianrunner
#17 h  Apr 11, 2025, 4:43 AM • 1 Y
Y by idk12345678
idk12345678 wrote:
martianrunner wrote:
by the way I may have given off the wrong vibe with my comment, I apologize

the questions are very well-written, I really enjoyed the test

good job :)

thanks. you can dm me your answers and i can grade them if you want, and then u can be on the leaderboard

I still haven't finished p6 (I was only able to do p1 to p5 in the timeframe - to be honest I kinda wasted some of my time just doodling around on my paper lol)

I'll send everything tomorrow (p6 won't be counted)
This post has been edited 1 time. Last edited by martianrunner, Apr 11, 2025, 4:45 AM
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idk12345678
381 posts
idk12345678
#18 h  Apr 14, 2025, 2:11 PM
Y by
SUBMISSION DEADLINE in 48 HOURS
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crazydog
18 posts
crazydog
#19 h  Apr 15, 2025, 12:51 AM • 1 Y
Y by idk12345678
\signup crazydog
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idk12345678
381 posts
idk12345678
#20 h  Apr 15, 2025, 1:03 AM
Y by
NEW SUBMISSION DEADLINE: 4/19 8AM MDT
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idk12345678
381 posts
idk12345678
#21 h  Apr 15, 2025, 3:25 AM
Y by
Correction: On #1 its supposed to say y not x for the answer. Also #4 is a sum of sums, not a product of sums.
This post has been edited 1 time. Last edited by idk12345678, Apr 15, 2025, 3:33 AM
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crazydog
18 posts
crazydog
#22 h  Apr 15, 2025, 4:04 AM
Y by
Click to reveal hidden text
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idk12345678
381 posts
idk12345678
#23 h  Apr 15, 2025, 1:25 PM
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Leaderboard
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idk12345678
381 posts
idk12345678
#25 h  Apr 18, 2025, 4:23 PM
Y by
Leaderboard
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mathprodigy2011
318 posts
mathprodigy2011
#26 h  Apr 18, 2025, 10:47 PM
Y by
idk12345678 wrote:
Leaderboard

for p5 if u plug in y=0 then you get f(x)=f(f(0))-f(0) which is a constant value but the function isnt constant?
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idk12345678
381 posts
idk12345678
#27 h  Apr 19, 2025, 12:48 AM
Y by
mathprodigy2011 wrote:
idk12345678 wrote:
Leaderboard

for p5 if u plug in y=0 then you get f(x)=f(f(0))-f(0) which is a constant value but the function isnt constant?

my bad, fixed it in the clarificaitons. I will release solutions this weekend after the deadline
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vsarg
260 posts
vsarg
#29 h  Apr 19, 2025, 3:16 AM
Y by
How is that spam? It is valuable advice that doesn't need to be pointed out as spam by you thinking you are a police officer in sunglasses. I understand you think such information is unimportant and only for the use of postfarming but I think that they posted to point out their mistake. I used grammarly so i dont think i have spellingn issues. Nvm post got deleted
This post has been edited 1 time. Last edited by vsarg, Apr 20, 2025, 2:52 AM
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