[/quote]
,
board, there is initially a tree of height 
.
.
such that the gardener can ensure there are eventually 
,![\[\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\geq 4+\frac{8(a-c)^2}{(a+b+c+d)^2}.\]](http://latex.artofproblemsolving.com/7/b/6/7b6e32d32d89ca058a06974e7276f0a5874d90a7.png)
such that the equation
be a positive integer and 
be a polynomial with integer coefficients such that 
.
is divisible by 
.
such that for every positive real 
,
satisfying![\[
\frac{\varphi(n!)}{n^\alpha\,(n-1)!} \;>\; c.
\]](http://latex.artofproblemsolving.com/4/4/4/4443cf7166cc65e67e2e504a826c4ac5f91aab2b.png)
be a positive integer and let 
be a strictly increasing sequence of 
be a subset of 
such that the value of![\[
\left|1-\sum_{i \in X} a_{i}\right|
\]](http://latex.artofproblemsolving.com/2/5/1/2515e074de1782f38453e1fce8ab7c2ec7cfe4c0.png)
is minimised. Prove that there exists a strictly increasing sequence of 
with sum equal to 2 such that![\[
\sum_{i \in X} b_{i}=1.
\]](http://latex.artofproblemsolving.com/3/7/4/37410820fc4c546f11d57212cfce53a7ec4941e3.png)
be a scalene triangle with circumcircle 
,
at 
.
meets 
and 
.
intersects the 
-
,
,
.
passes through either 
be positive real numbers such that : 
. Prove that : 
.
?
![$P, Q \in \mathbb{R}[x]$](http://latex.artofproblemsolving.com/c/3/0/c301578bade5b93056d77454921cba0a9812212c.png)
be relatively prime nonconstant polynomials. Show that there can be at most three real numbers 
such that 
is the square of a polynomial.
Y by Cattus1221, lpieleanu, jkim0656, Alex-131, justJen, EpicBird08, littlefox_amc, blueprimes, deduck, Exponent11, alan9535, aidan0626
Hey! I got accepted into Ross Indiana, and I think I'll probably also get accepted into HCSSiM. I've been looking between the two camps, and I'm trying to decide which one to go to -- both seem like really fun options.
Instead of trying to explain my personal preferences and thought processes, I thought it might be a good idea to ask the community for their personal opinions on these camps. What are some things that you like or dislike about both camps? (Whether it be through personal experience or by word-of-mouth, but please specify if it's just something you've heard)
This will probably help me be more informed on making a final decision, so I'd appreciate any advice. Thanks in advance!
Instead of trying to explain my personal preferences and thought processes, I thought it might be a good idea to ask the community for their personal opinions on these camps. What are some things that you like or dislike about both camps? (Whether it be through personal experience or by word-of-mouth, but please specify if it's just something you've heard)
This will probably help me be more informed on making a final decision, so I'd appreciate any advice. Thanks in advance!
This post has been edited 1 time. Last edited by akliu, Apr 18, 2025, 6:20 PM
Reason: probably definitely
Reason: probably definitely
.
