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
,
lying inside the rhombus and satisfying 
.
, such that 
Prove that :
equality cases : ?
isomorphic to 
?
be a 
be a prime number?
,
statements are equivalent:
is differentiable, with continuous first derivative.
and for any two sequences 
,
,
for any positive integer 
,
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 
.
;
,
.
Y by Adventure10
Given is the triangle 
, with 
. Let's denote 
also points that 
and 
are parallelograms. On the sides 
and 
sides, 
and 
are selected respectively so that 
. Prove that the lines 
and 
intersect at the line segment 
, with 
. Let's denote 
also points that 
and 
are parallelograms. On the sides 
and 
sides, 
and 
are selected respectively so that 
. Prove that the lines 
and 
intersect at the line segment 
This post has been edited 2 times. Last edited by parmenides51, Mar 14, 2020, 3:03 PM
be the reflection of 
across 
and 
is the reflection of 
be a point on 
and 
.
and 
are collinear, similarly 
are collinear.
and it is true because 
.
