,
such that 
(i.e: sum of powers of point 
b
and 
on 
and 
are on the same side of 
be midpoint of segment 
be midpoint of segment 
be intersection of 
with 
and 
![\[
\max(a_1, a_2) + \max(a_2, a_3), + \dots + \max(a_{n-1}, a_n) + \max(a_n, a_1),
\]](http://latex.artofproblemsolving.com/4/c/b/4cba741142419b031efdeba713748762fa6b2aac.png)
where 
runs over the set of permutations of 
.
,
denote the integers modulo ![$\mathbb{F}_p[x]$](http://latex.artofproblemsolving.com/e/5/a/e5a21492095c9116b100e2f7626a70cc26834e82.png)
be the set of polynomials with coefficients in ![$P(x) \in \mathbb{F}_p[x]$](http://latex.artofproblemsolving.com/7/a/a/7aa574df0669ce78536b1ecc5c949120aa2b3009.png)
such that for all integers 
such that 
.
quartic polynomials in 
Is there any reason why we shouldn't write 
instead?
has at most one solution continuous for 
)
is a fixed real number. (A. 7)
converge?
,
where 
is the identity matrix. If for some matrix 
is identity, does it follow that 
be real numbers. Find the ranges of 
converges.
are group. If 
,
or 
.
are complex numbers such that
and if 
denotes the sum of all products of these 
at a time, prove that
whenever the denominator of the left-hand side is different from 
.
for any positive reals satifying 
?
Y by MathsMadman, mathematicsy, cubres
Players A and B play a game. They are given a box with 
candies. A starts first. On a move, if in the box there are 
candies, the player chooses positive integer 
so that 
and 
, and eats candies from the box. The player who eats the last candy wins. Who has winning strategy, in terms of 
.
candies. A starts first. On a move, if in the box there are 
candies, the player chooses positive integer 
so that 
and 
, and eats candies from the box. The player who eats the last candy wins. Who has winning strategy, in terms of 
.This post has been edited 2 times. Last edited by VicKmath7, Mar 11, 2020, 11:19 AM
candies and eat them so he wins(except for 
where he obviously wins).for even 
.
is odd number.
candles remained.Second eats 1 and first eats the last one and wins.
is even.
candles and wins...
,
they simply take 
