The elementary symmetric functions of a reciprocal polynomial sequence

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• 作者：Yuanyuan Luo^a ; ^{yuanyuanluoluo@163.com" class="auth_mail} ; Shaofang Hong^a ; ¹ ; ^{sfhong@scu.edu.cn" class="auth_mail} ; ^{s-f.hong@tom.com" class="auth_mail} ; ^{hongsf02@yahoo.com" class="auth_mail} ; Guoyou Qian^b ; ² ; ^{qiangy1230@163.com" class="auth_mail} ; ^{qiangy1230@gmail.com" class="auth_mail} ; Chunlin Wang^a ; ^{wdychl@126.com" class="auth_mail}
• 刊名：Comptes Rendus Mathematique
• 出版年：April, 2014
• 年：2014
• 卷：352
• 期：4
• 页码：269-272
• 全文大小：188 K

文摘

Erd枚s and Niven proved in 1946 that for any positive integers m and d, there are at most finitely many integers n for which at least one of the elementary symmetric functions of are integers. Recently, Wang and Hong refined this result by showing that if , then none of the elementary symmetric functions of is an integer for any positive integers m and d. Let f be a polynomial of degree at least 2 and of nonnegative integer coefficients. In this paper, we show that none of the elementary symmetric functions of is an integer except for with being an integer and .