[/quote]
,
such that 
for all 
?
be a monic polynomial with complex coefficients such that there exist a polynomial 
with complex coefficients for which ![\[P(x^2-2)=P(x)Q(x).\]](http://latex.artofproblemsolving.com/a/6/2/a62b06890b6bbcc5c9634f6de8c7ae5fe9f37828.png)
Determine all complex numbers that could be the root of 
and 
Prove that
Prove that
such that for all 
,![\[xf(x+f(y))=(y-x)f(f(x)).\]](http://latex.artofproblemsolving.com/e/4/a/e4a3bbb8b91d2aa62d699c24df342fa59be71915.png)
.
such that for all 
,![\[
f(xf(x+y)+z) = f(z) + f(x)y + f(xf(x)).
\]](http://latex.artofproblemsolving.com/f/9/3/f93b7526ff4338eea89a1c59bc009aa001ffc15d.png)
of integers that has the following property:
(possibly 
)
for every integer 
.
of nonzero integers such that the only admissible set containing both 
and 
is the set of all integers.
be the circumcenter and orthocenter of triangle 
,
and 
intersect at point 
.
is an arbitrary point on
and 
be the intersection of 
w
and 
, respectively.
are concyclic.
with incenter 
.
and 
intersects 
and 
and 
,
and 
be the midpoints of 
meets the external bisector of angle 
at 
and line 
meets the external bisector of angle 
at 
.
are concylic.
be the nonnegative integers in 
where 
.
.
.
such that 
where 
,
?
where 
,
satisfying
Prove
at 
and 
is the circumcenter of 
.
.
Y by
In the pyramid 
the length of the edge AB is equal to 
cm, and the length of the edge 
with 
cm. The distance between the lines 
and is equal to 
cm. Determine the measure of the angle formed by the lines and , if it is known that the volume of the pyramid is equal with 
cm
the length of the edge AB is equal to 
cm, and the length of the edge 
with 
cm. The distance between the lines 
and is equal to 
cm. Determine the measure of the angle formed by the lines and , if it is known that the volume of the pyramid is equal with 
cm
