[/quote]
,
denote the sum of the 
t
.
,
,
.
,
,
be real numbers such that 
for 
,
,
What is 
?
by 
different methods. The same inequality can be used twice but in different ways, dm me if you have any question about the rules.
intersect at 
,
tangent to the extensions of 
at 
respectively. Circle 
passes through points 
,
.
.
let 
be the foot of the altitude from 
to the side 
and 
,
,
be the incenter, 
-
and 
the other intersection points of the circle 
with the lines 
and 
,
.
be a set that intersects all non-finite integer arithmetic progressions, 
be the set of prime divisors of 
and 
be the set of prime divisors of 
.
.
,
be a triangle, and let 
be centered at 
,
and tangent to line 
,
intersect 
again at 
and let line 
intersect 
again at 
.
is the other intersection of the circumcircles of triangles 
,
,
either concur or are all parallel.
and 
are the points of tangency of incircle with the center of 
and 
be the foot of the perpendicular from 
.
such that 
.
is the orthocenter of 
,
bisects 
.
,
are reals. Let 
and let 
meets the x-axis again at 
.
denote the midpoints of 
.
.
.
,
(where 
can be 0), and let 
such that 
and 
is considered the same as 
)
is 
,
,
,
are positive integers, and 
are odd primes.
be positive integers, and let 
all be 
-![\[
\alpha_1^j + \alpha_2^j + \cdots + \alpha_n^j = 0 \quad \text{for any } j (0 < j < k).
\]](http://latex.artofproblemsolving.com/3/3/b/33be8eef29cd506bf1132a86def9992ec8d21cb4.png)
Prove that among 
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For the third summer in a row, the Junior Mathematicians' Problem Solving Competition (JMPSC) team brings you our contest on August 19th! This year will be open to all high schoolers, middle schoolers, and elementary schoolers.
Sign up here and find out more at our website, which contains sample problems from last year's competition.
The Contest
System:
This year, JMPSC offers two divisions, each of which contains two rounds. To qualify for the final round, participants must be in the upper half of contestants.
Division II is meant to be accessible for EVERYONE, even those who have never heard of competition math before. (Great way to introduce your friends to competition math!) Final placements and prize winners are decided first by scores, then by the speed of submission (although due to the weightings, ties will most likely be irrelevant).
Times: The contest will be held from 10:00 AM - 1:00 PM PST on August 19th.
Platform: JMPSC will be hosted on google meets. Further instructions will be sent once you sign up on this google form.
Eligibility: This year will be open to all high schoolers, middle schoolers, and elementary schoolers.
Website/Contact
For more information, please visit our website that explains the contest logistics in-depth and provides some sample problems for contestants to gauge the overall difficulty of our problems. Please use the contact form or use one of the emails listed if you have any questions.
Prizes
Thanks to our generous sponsors, we will be able to hand out over $5000 worth of prizes to each of:
- Division I:
- $250 given to first place winner
- $125 given to second place winner
- $100 given to third place winner
- One 3B1B plushie and one 3B1B math notebook to each of fourth, fifth, and sixth place
- $25 AoPS Coupon to seventh and eighth place
- 20 Wolfram Alpha Notebook subscriptions to the first twenty winners
- $45 Desmos gift shop (raffle)
- Division II:
- $100 given to first place winner
- $75 given to second place winner
- $50 given to third place winner
- One 3B1B plushie and one 3B1B math notebook to each of fourth, fifth, and sixth place
- $25 AoPS Coupon to seventh and eighth place
- 20 Wolfram Alpha Notebook subscriptions to the first twenty winners
- One $399 Daily Challenge Courses (raffle)
Sponsors
I'd rather have his permission to share his score.
)
