MASON-STOTHERS THEOREM AND PERFECT BINARY POLYNOMIALS

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

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