In an earlier issue of Mathematical Reflections, Iurie Boreico (from Harvard) proposed the following problem.
Problem: A polynomial is called a “mirror” if . Let and consider polynomials such that , and . Prove that is a mirror iff is a mirror.
Two solutions – the pdf file size is around 1 Mb – to the above problem were proposed, and the one by the author is very close to the one I had worked out myself (partially) earlier but never really got around finishing it. So, I will post my solution here but at a slightly later time. In the meantime, you might be interested in finding a solution yourself.