Mythical numbers.

Bázlik, Miro

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Displaying similar documents to “Mythical numbers.”

On the number of prime factors of a finite arithmetical progression

T. N. Shorey, R. Tijdeman (1992)

Acta Arithmetica

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Perfect powers in products of terms in an arithmetical progression III

T. N. Shorey, R. Tijdeman (1992)

Acta Arithmetica

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On Robin’s criterion for the Riemann hypothesis

YoungJu Choie, Nicolas Lichiardopol, Pieter Moree, Patrick Solé (2007)

Journal de Théorie des Nombres de Bordeaux

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Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality $σ (n) : = \sum_{d | n} d < e^{γ} n log log n$ is satisfied for $n \geq 5041$ , where $γ$ denotes the Euler(-Mascheroni) constant. We show by elementary methods that if $n \geq 37$ does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that $n$ must be divisible by a fifth power $> 1$ . As consequence we obtain that RH holds true iff every natural number divisible by...

Palindromic powers.

Hernández, Santos Hernández, Luca, Florian (2006)

Revista Colombiana de Matemáticas

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Integer sequences, functions of slow increase, and the Bell numbers.

Jakimczuk, Rafael (2011)

Journal of Integer Sequences [electronic only]

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An arithmetic function arising from Carmichael’s conjecture

Florian Luca, Paul Pollack (2011)

Journal de Théorie des Nombres de Bordeaux

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Let $φ$ denote Euler’s totient function. A century-old conjecture of Carmichael asserts that for every $n$ , the equation $φ (n) = φ (m)$ has a solution $m \neq n$ . This suggests defining $F (n)$ as the number of solutions $m$ to the equation $φ (n) = φ (m)$ . (So Carmichael’s conjecture asserts that $F (n) \geq 2$ always.) Results on $F$ are scattered throughout the literature. For example, Sierpiński conjectured, and Ford proved, that the range of $F$ contains every natural number $k \geq 2$ . Also, the maximal order of $F$ has been investigated by Erdős and Pomerance....

Equations involving arithmetic functions of factorials.

Luca, Florian (2000)

Divulgaciones Matemáticas

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On a problem of Fujii concerning Riemann's $ζ$ -function.

Puchta, J.-C. (2001)

Acta Mathematica Universitatis Comenianae. New Series

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A bound for the torsion in the $K$ -theory of algebraic integers.

Soulé, Christophe (2003)

Documenta Mathematica

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