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and distinct positive integers 
are given. Does there exist a polynomial ![$p(x)\in\Bbb{Z}[x]$](http://latex.artofproblemsolving.com/5/1/a/51a23efd70e495d2fe516b642f0a6e71e5875ba2.png)
of degree 
that satisfies the following conditions?
of positive integers such that
, find the locus of the points 
lying inside the rhombus and satisfying 
.
, such that 
Prove that :
equality cases : ?
be a Chebyshev polynomial of the second kind. If n>2 and x > 2 is a integer, Could 
be a prime number?
, the following 
statements are equivalent:
is differentiable, with continuous first derivative.
and for any two sequences 
, convergent to 
, such that 
for any positive integer 
, the sequence 
is convergent.
![\[F(x)=\int\limits_0^{x}\left(\sin\frac 1t\right)^4\mathrm dt.\]](http://latex.artofproblemsolving.com/1/c/2/1c2359167d0bfb8af7d7e1f93984c195e5fb1971.png)
Determine the value of 
be two matrices such that 
. Prove that: is odd, then 
;
, then .
be points in the sides 
of 
respectively. The quadrilateral 
has an incircle of radius 
, if the incircles of 
and 
also have the radius . Prove that
isomorphic to 
?
.