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On the divisor function d(n)

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  26 February 2010

Jiahai Kan  and
Zun Shan
Jiahai Kan
Affiliation:
Nanjing Institute of Posts and Telecommunications, 210003 Nanjing, Nanjing, China.
Zun Shan
Affiliation:
Department of MathematicsNanjing Normal University, 210097 Nanjing, Nanjing, China.
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Extract

In 1984 Heath-Brown [5] proved the following conjecture of Erdős and Mirsky [2] (which seemed at one time as hard as the twin prime problem):

“There exist infinitely many integers n for which d(n) = d(n + 1).”

MSC classification

Secondary: 11K65: Arithmetic functions
Type
Research Article
Information
Mathematika , Volume 43 , Issue 2 , December 1996 , pp. 320 - 322
Copyright
Copyright © University College London 1996

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References

1.Chen, J.. On the representation of a large even integer as the sum of a prime and the product of at most two primes. Sai. Sinica, 16 (1973). 157–176.Google Scholar
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5.Heath-Brown, D. R.. The divisor function at consecutive integers. Mathematika, 31 (1984), 141–149.Google Scholar
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8. J. Kan. On the number of solutions of N − p = P r. J. reine und angew. Math., 414 (1991), 117–130.Google Scholar