[/quote]
,
,
.
that satisfies:
such that 
is a perfect square.
such that, for every positive integer 
the integer
is a multiple of 
(Note that 
denotes the greatest integer less than or equal to 
For example, 
and 
)
If the value of 
can be written as 
where m and n are co-prime positive integers then find the value of 
If we set 
then it's the unique polynomial such that for all integers 
In general, for each positive integer k,there is a unique polynomial 
such that 
Find the value of 
for 
and 
if 
then find the coefficient of 
in 
such that:
be a prime and 
a nonempty set. Suppose that for each element 
there exist elements 
,
such that 
is divisible by 
,
denotes the cardinality of 
.
,
,
is divided into cyclic quadrilaterals with pairwise disjoint interiors. None of the vertices of the cyclic quadrilaterals in the decomposition is an interior point of a side of any cyclic quadrilateral in the decomposition or of a side of the quadrilateral 
.
is an integer. Is it true that for each perfect polynomial 
so that for each integer 
for which 
Y by Adventure10, Mango247
Let 
be a triangle, and let 
and 
be the feet of its altitudes issuing from the vertices 
and 
, respectively. Denote by 
the midpoint of the segment 
. The circumcircles of triangles 
and 
have a common point apart from ; denote this common point by 
. Prove that:
(a) The point lies on the circumcircle of the triangle .
(b) The line
passes through the point 
.
(c) We have
.
Darij
be a triangle, and let 
and 
be the feet of its altitudes issuing from the vertices 
and 
, respectively. Denote by 
the midpoint of the segment 
. The circumcircles of triangles 
and 
have a common point apart from ; denote this common point by 
. Prove that:(a) The point
lies on the circumcircle of the triangle .(b) The line
passes through the point 
.(c) We have
.Darij
.
.
.
.
and 
is the same.
we have 
.
.
we have the relaction 
.
,
)
