Find the range of values that can be taken by :
are positive reals.
there are elements 
such that 
.
would be divisible by 
for any integer values of 
,
is not a factor of 
be an integer. In a configuration of an 
board, each of the 
cells contains an arrow, either pointing up, down, left, or right. Given a starting configuration, Turbo the snail starts in one of the cells of the board and travels from cell to cell. In each move, Turbo moves one square unit in the direction indicated by the arrow in her cell (possibly leaving the board). After each move, the arrows in all of the cells rotate 
counterclockwise. We call a cell good if, starting from that cell, Turbo visits each cell of the board exactly once, without leaving the board, and returns to her initial cell at the end. Determine, in terms of 
,
Y by
Let 
be a point and let k be a circle through . Let 
and 
be two more points on 
. Let 
be the intersection of the bisector of 
with . Let 
be the reflection of wrt point , and 
the intersection of the straight line 
with . Prove that point is independent of the choice of and on the circle .
be a point and let k be a circle through . Let 
and 
be two more points on 
. Let 
be the intersection of the bisector of 
with . Let 
be the reflection of wrt point , and 
the intersection of the straight line 
with . Prove that point is independent of the choice of and on the circle .
of 
and 
are collinear, we get 
and 
