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, Mango247
Given an isosceles triangle 
with base 
. Point 
is taken on the extension of the side 
(beyond the point 
) so that 
. Denote 
the intersection point of angle - bisectors of 
and 
. Lines and 
intersect at point 
, lines 
and 
intersect at point 
. Prove that line 
passes through the midpoint of the segment 
.
with base 
. Point 
is taken on the extension of the side 
(beyond the point 
) so that 
. Denote 
the intersection point of angle - bisectors of 
and 
. Lines and 
intersect at point 
, lines 
and 
intersect at point 
. Prove that line 
passes through the midpoint of the segment 
.This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 2:27 AM
