MASON-STOTHERS THEOREM AND PERFECT BINARY POLYNOMIALS

Authors : Luis H GALLARDO

Pages : 1-8

Doi:10.24330/ieja.768086

View : 11 | Download : 10

Publication Date : 2020-07-14

Article Type : Research Paper

Abstract :We prove that there is no perfect binary polynomial $R$ that is the sum of two appropriate powers, besides, possibly $R=P+1$ with $P$ irreducible. The proofs follow from analogue results involving the ABC-theorem for polynomials and a classical identity. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
Keywords : Polynomial ABC theorem, binary polynomial, perfect polynomial