Salajan's conjecture on discriminating terms in an exponential sequence

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• 作者：Pieter Moree^a ; ^{moree@mpim-bonn.mpg.de" class="auth_mail" title="E-mail the corresponding author} ; Ana Zumalacá ; rregui^b ; ^{a.zumalacarregui@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11T22 ; 11B83
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：160
• 期：Complete
• 页码：646-665
• 全文大小：421 K

文摘

Given a sequence of distinct positive integers v₁,v₂,…$v_1,v_2,\dots$ and any positive integer n  , the discriminator D_v(n)$D_v(n)$ is defined as the smallest positive integer m   such that a46a3fe08d9d6c" title="Click to view the MathML source">v₁,…,v_n$v_1,\dots ,v_n$ are pairwise incongruent modulo m  . We consider the discriminator for the sequence u₁,u₂,…$u_1,u_2,\dots$ , where u_j$u_j$ equals the absolute value of ((−3)^j−5)/4$({(-3)}^j-5)/4$, that is 26acff7372e2eb1" title="Click to view the MathML source">u_j=(3^j−5(−1)^j)/4$u_j=(3^j-5{(-1)}^j)/4$. We prove a 2012 conjecture of Sabin Salajan characterizing the discriminator of the sequence u₁,u₂,…$u_1,u_2,\dots$ .