Y by
A polynomial
with degree
is reflexive if there is an integer
such that
for every
, where
for
. Let
be an integer and
be a polynomial with integer coefficients. Prove that there exist reflexive polynomials
,
with integer coefficients such that
![\[(1+x+x^2+\dots+x^{\ell-1})p(x)=q(x)+x^\ell r(x)\]](//latex.artofproblemsolving.com/6/6/7/66729b54a8b87c6ddbfdf7e7e5932dbb8b262439.png)











![\[(1+x+x^2+\dots+x^{\ell-1})p(x)=q(x)+x^\ell r(x)\]](http://latex.artofproblemsolving.com/6/6/7/66729b54a8b87c6ddbfdf7e7e5932dbb8b262439.png)