- International Electronic Journal of Algebra
- Vol: 28 Issue: 28
- MASON-STOTHERS THEOREM AND PERFECT BINARY POLYNOMIALS
MASON-STOTHERS THEOREM AND PERFECT BINARY POLYNOMIALS
Authors : Luis H. Gallardo
Pages : 1-8
Doi:10.24330/ieja.768086
View : 10 | Download : 8
Publication Date : 2020-07-14
Article Type : Research
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