Uniform lower bound for the least common multiple of a polynomial sequence

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• 作者：Shaofang Hong ; Yuanyuan Luo ; Guoyou Qian ; Chunlin Wang
• 刊名：Comptes Rendus Mathematique
• 出版年：November, 2013
• 年：2013
• 卷：351
• 期：21-22
• 页码：781-785
• 全文大小：226 K

文摘

Let n be a positive integer and be a polynomial with nonnegative integer coefficients. We prove that , except that and and that , with being an integer and , where denotes the smallest integer, which is not less than . This improves and extends the lower bounds obtained by M. Nair in 1982, B. Farhi in 2007 and S.M. Oon in 2013.