On stronger conjectures that imply the Erdős–Moser conjecture

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• 作者：B.C. Kellner<sup>asup><sup> ; sup><sup>bk@bernoulli.orgsup>
• 关键词：Erd&#x151 ; s– ; Moser equation ; Consecutive values of polynomials
• 刊名：Journal of Number Theory
• 出版年：2011
• 出版时间：June 2011
• 年：2011
• 卷：131
• 期：6
• 页码：1054-1061
• 全文大小：132 K

文摘

The Erd&#x151;s–Moser conjecture states that the Diophantine equation S<sub>ksub>(m)=m<sup>ksup>, where S<sub>ksub>(m)=1<sup>ksup>+2<sup>ksup>++(m−1)<sup>ksup>, has no solution for positive integers k and m with k2. We show that stronger conjectures about consecutive values of the function S<sub>ksub>, that seem to be more naturally, imply the Erd&#x151;s–Moser conjecture.