Displaying similar documents to “Equations involving arithmetic functions of factorials.”

Mythical numbers.

Bázlik, Miro (2009)

Acta Mathematica Universitatis Comenianae. New Series

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Power-free values, large deviations, and integer points on irrational curves

Harald A. Helfgott (2007)

Journal de Théorie des Nombres de Bordeaux

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Let f ∈ ℤ [ x ] be a polynomial of degree d ≥ 3 without roots of multiplicity d or ( d - 1 ) . Erdős conjectured that, if f satisfies the necessary local conditions, then f ( p ) is free of ( d - 1 ) th powers for infinitely many primes p . This is proved here for all f with sufficiently high entropy. The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem from the theory of large deviations. ...

Some solved and unsolved problems in combinatorial number theory, ii

P. Erdős, A. Sárközy (1993)

Colloquium Mathematicae

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In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.