[/quote]
,
be the orthocenter of acute triangle 
,
be the foot of the altitude from 
to 
,
be the reflection of 
.
intersects line 
and 
.
.
of positive integers such that 
and 
are both powers of 
.
the set of all positive real numbers.
which have the property:![\[f(x)f(y)=2f(x+yf(x))\]](http://latex.artofproblemsolving.com/4/f/f/4ffbde35ff082585a188c1a4368d39338d1b07a4.png)
and 
.
be a function that satisfies the following equation for all real numbers 
:![\[
f(x^2 + x + 3) + 2f(x^2 - 3x + 5) = 6x^2 - 10x + 17.
\]](http://latex.artofproblemsolving.com/f/6/2/f625b922656061221157fdb5a3b958cfa7d57108.png)
Find the value of 
.
and 
such that 
for all positive integers 
.
and 
.![$\sqrt[3]{ab-1}+\sqrt[3]{bc-1}+\sqrt[3]{ca-1} \le \sqrt[3]{(a+b+c)^2}$](http://latex.artofproblemsolving.com/9/6/3/9633b5849794285e44519c745c1f616eceb77711.png)
consecutive even numbers, such that the square of their product is divisible by the sum of their squares.
such that among any 
positive real numbers 
with 
,
.
Let 
.
prime and 
a positive integer. Determine all pairs 
satisfying the equation: 
be a positive integer and let 
and 
be sets of integers satisfying the following conditions:
,
and 
,
iff 
be the set of integers, and let 
be a function. Prove that there are infinitely many integers 
such that the function 
defined by 
is not bijective.
,
such that 
.
Y by KevinYang2.71, OronSH, aliz, Pengu14, vincentwant, EpicBird08, llbaobao
Can someone explain to me how this is a zero and not a 5? I wrote the Vieta's equivalent of "two consec zero coefficients", which was worth 5 points
I messed up the numbering and I believe that is the underlying cause of the misgrade but if someone sees any other error, please let me know so I don't wrongly email MAA.
Update: I posted this while flipping out upon seeing a zero on my P2 wanting to find a way to somehow appeal - it genuinely felt like 24JMO4 all over again. Thankfully, this -5 did not game-end my score this year
I messed up the numbering and I believe that is the underlying cause of the misgrade but if someone sees any other error, please let me know so I don't wrongly email MAA.
Update: I posted this while flipping out upon seeing a zero on my P2 wanting to find a way to somehow appeal - it genuinely felt like 24JMO4 all over again. Thankfully, this -5 did not game-end my score this year
Attachments:
This post has been edited 6 times. Last edited by Mathandski, Apr 23, 2025, 12:01 AM
