MathDB
Sequence of trinomials?

Source: Tuymaada 2021 Senior P8

July 28, 2021
polynomialquadraticsalgebrarational functions

Problem Statement

In a sequence PnP_n of quadratic trinomials each trinomial, starting with the third, is the sum of the two preceding trinomials. The first two trinomials do not have common roots. Is it possible that PnP_n has an integral root for each nn?