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A GENERALISATION OF A THEOREM OF ERDŐS AND NIVEN
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 106 / Issue 2 / October 2022
- Published online by Cambridge University Press:
- 24 January 2022, pp. 215-223
- Print publication:
- October 2022
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- Article
- Export citation
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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.
