,
.
satisfies the quadratic equation 
and deduce that the value of 
.
.
,
is 
.
"
![$f \in C^1([0,1]), g \in C^2(f([0;1]))$](http://latex.artofproblemsolving.com/f/5/2/f52369171ef8571734950120c43aacac10154fcd.png)
.
?
,
are positive integers and 
is odd.
and 
.
with multiplication of matrixes operation is making an isomorphic-group structure with 
.
.
p
a
and the line 
.
by 
and 
for all 
,
Show that 
is an integer for all 
.
,
by the inequality
,
and 
.
from 
to 
and 
from 
to 
but in vain.
and integers 
such that 
Y by AIME12345, JasperL, kingofgeedorah, 62861, Magikarp1, Generic_Username, budu, mathisawesome2169, checkmatetang, laegolas, speck, Mudkipswims42, rkm0959, skipiano, itised, zxcv1337, anantmudgal09, ThisIsASentence, algebra_star1234, PiDude314, champion999, Plasma_Vortex, artsolver, atmchallenge, Kaladesh, PcelicaMaja, CaptainFlint, AlgebraFC, brianapa, huricane, Problem_Penetrator, leequack, kk108, countdown1234, mathwizard888, soojoong, MinionSV, don2001, niyu, parmenides51, amar_04, AmirKhusrau, OlympusHero, myh2910, Adventure10
"If it is GGG, it will be GG..."
The contest is over!
Welcome, everyone! Over the last few weeks, I have had the pleasure of creating another olympiad geometry contest. My first one can be found here.
As users last time complained about the difficulty of 1/4, I've intentionally made 1/4 around JMO 1/4 level; 2/5/3/6 are closer to USAMO than USAJMO.
I'd like to thank users Generic_Username, AlgebraFC, MathSlayer4444, InCtrl, champion999, joey8189681, braniac1 for being there to support me in the creation of this contest. As well as complaining about the difficulty of drawing the diagrams, they also provided moral support and, in some cases, testsolved problems.
I have already recruited enough testsolvers, and I'd like to thank all who signed up to do so. Their usernames can be found below. Unfortunately, as JMO day I demonstrated, I still don't consider myself adequately good at bash to grade bash solutions, so I need people willing to grade ugly, ugly solutions. PM me if you want to grade bash solutions, or just post below!
See this post about time limits.
Congratulations to EulerMacaroni, tastymath75025, SAUDITYA, rkm0959, mofumofu, and huricane for winning the contest with perfect scores, and congratulations to PcelicaMaja and B.J.W.T for earning second place!
The contest is over!
Welcome, everyone! Over the last few weeks, I have had the pleasure of creating another olympiad geometry contest. My first one can be found here.
As users last time complained about the difficulty of 1/4, I've intentionally made 1/4 around JMO 1/4 level; 2/5/3/6 are closer to USAMO than USAJMO.
I'd like to thank users Generic_Username, AlgebraFC, MathSlayer4444, InCtrl, champion999, joey8189681, braniac1 for being there to support me in the creation of this contest. As well as complaining about the difficulty of drawing the diagrams, they also provided moral support and, in some cases, testsolved problems.
I have already recruited enough testsolvers, and I'd like to thank all who signed up to do so. Their usernames can be found below. Unfortunately, as JMO day I demonstrated, I still don't consider myself adequately good at bash to grade bash solutions, so I need people willing to grade ugly, ugly solutions. PM me if you want to grade bash solutions, or just post below!
See this post about time limits.
Congratulations to EulerMacaroni, tastymath75025, SAUDITYA, rkm0959, mofumofu, and huricane for winning the contest with perfect scores, and congratulations to PcelicaMaja and B.J.W.T for earning second place!
This post has been edited 36 times. Last edited by wu2481632, Jun 21, 2017, 4:09 AM
