Papers › On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}
On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}
Weilin Zhang, Hongjian Li, Sunben Chiu, Pingzhi Yuan
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In 1946, P. Erd\H{o}s and I. Niven proved that there are only finitely many positive integers n for which one or more of the elementary symmetric functions of 1,1 / 2, ⋯, 1 / n are integers. In 2012, Y. Chen and M. Tang proved that if n ⩾4, then none of the elementary symmetric functions of 1,1 / 2, ⋯, 1 / n are integers. In this paper, we prove that if n ⩾5, then none of the elementary symmetric functions of {1,1 / 2, ⋯, 1 / n} \{1 / i} are integers except for n=i=2 and n=i=4.
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