A GENERALISATION OF A THEOREM OF ERDŐS AND NIVEN
Bulletin of the Australian Mathematical Society(2022)
摘要
In 1946, Erdős and Niven proved that no two partial sums of the harmonic series can be equal. We present a generalisation of the Erdős–Niven theorem by showing that no two partial sums of the series $\sum _{k=0}^\infty {1}/{(a+bk)}$ can be equal, where a and b are positive integers. The proof of our result uses analytic and p-adic methods.
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关键词
p-adic valuation,arithmetic progression,partial sum,harmonic series,Diophantine equation,unit fraction
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