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Gaps between consecutive divisors of factorials

Daniel Berend, J. E. Harmse (1993)

Annales de l'institut Fourier

The set of all divisors of n ! , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest n ! and obtain a lower bound on their distance.

Gaps between primes in Beatty sequences

Roger C. Baker, Liangyi Zhao (2016)

Acta Arithmetica

We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).

Generalization of a theorem of Steinhaus

C. Cobeli, G. Groza, M. Vâjâitu, A. Zaharescu (2002)

Colloquium Mathematicae

We present a multidimensional version of the Three Gap Theorem of Steinhaus, proving that the number of the so-called primitive arcs is bounded in any dimension.

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