[/quote]
,
such that ![\[ \dfrac{a^2}{2ab^2-b^3+1} \]](http://latex.artofproblemsolving.com/0/d/2/0d2f10786d22af2ea94ebeed6b15e723f4042734.png)
is a positive integer.
?
be a triangle and let 
and 
be variable points on sides 
and 
,
.
denote the point on 
such that 
is parallel to 
,
denote the point on 
such that 
is parallel to 
.
vary, the circumcircle of 
passes through a fixed point, other than 
.
satisfy that 
.
![\[a_1\geq a_2\geq a_3\geq\cdots,\qquad b_1\geq b_2\geq b_3\geq\cdots\]](http://latex.artofproblemsolving.com/7/9/e/79e388eba20412905964dc2b4ebb491f3c79143b.png)
and the sums ![\[A_n = a_1 + \cdots + a_n,\quad B_n = b_1 + \cdots + b_n;\qquad n = 1,2,\ldots.\]](http://latex.artofproblemsolving.com/3/c/4/3c44766edcc9e5269f0d3396386e41676cbdf42c.png)
For any pair define 
and 
,
.
,
such that the sequences 
and 
are unbounded while the sequence 
is bounded?
,
?
,
.
lies on 
such that 
.
passing trough 
at 
.
.
be a positive integer. Find, in terms of 
with integer coefficients such that for every integer 
,
such that 
.
.
be the set of positive integers. A function 
satisfies the equation ![\[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]](http://latex.artofproblemsolving.com/2/e/7/2e73ff2f75b103e9d6a4004a42e4ed7f4ee64a67.png)
for all positive integers 
.
.
Y by blueprimes, Pengu14, Alex-131, Ultroid999OCPN
Registration is open until March 14! Find the form here.
Calling all SoCal high-school math students!
From the University of Southern California, the student-run Southern California Mathematics Competition (SCMC) returns for another year!
Contest info
We plan to hold our Spring 2025 contest on Saturday, 29 March, on USC's University Park Campus. This time we are going to introduce the online version! Competitors not in Socal area could select the online version.
However, the online competition will be considered unofficial; i.e. only onsite, in-person competitors will be eligible for awards, but we might still recognize the top scorers. Online competitors will compete in the Individual Round only. We will send out the Team Round problems after the conclusion of the Individual Round, but we will not be collecting answers to these problems or scoring them.
- The intended target audience for this competition is high-school students, but middle-school students are also welcome to participate!
- As is typical, our competition will feature both individual and team-based components: you may choose to compete individually or as part of a team of 4 students, although we strongly encourage you to compete with a team.
- This year we are going to have one division only. All competitors will compete in a 20-problem, 120-minute individual round with problems on topics in algebra, number theory, combinatorics, and geometry.
- Those competitors on a team will then compete in a 10-problem, 30-minute team round. One or more problems on the team round will feature content covered in a faculty lecture given on the day of the competition.
- Before the awards ceremony, we will have a head-to-head MATHCOUNTS Countdown Round-style contest (just for fun). Top 8 competitors face off head-to-head in single-elimination tournament.
Additionally, you may view samples of our past work here. If you're looking for resources to study, this page may also be of help.
Hope to see you there, and math on!
- Bluesoul, SCMC Competition Design Chair
