When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently

Claudia A. Spiro-Silverman

Displaying similar documents to “When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently”

On systems of composite Lehmer numbers with prime indices

J. Wójcik (1996)

Colloquium Mathematicae

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Lower bounds for the solutions in the second case of Fermat's equation with prime power exponents

Maohua Le (1993)

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Squares in Lucas sequenceshaving an even first parameter

Paulo Ribenboim, Wayne McDaniel (1998)

Colloquium Mathematicae

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On rough and smooth neighbors.

William D. Banks, Florian Luca, Igor E. Shparlinski (2007)

Revista Matemática Complutense

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We study the behavior of the arithmetic functions defined by F(n) = P⁺(n) / P^-(n+1) and G(n) = P⁺(n+1) / P^-(n) (n ≥ 1) where P⁺(k) and P^-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.

A note on primes p with $σ (p^{m}) = z^{n}$

Maohua Le (1991)

Colloquium Mathematicae

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Proth Numbers

Christoph Schwarzweller (2014)

Formalized Mathematics

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In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.

A note on a conjecture of Jeśmanowicz

Moujie Deng, G. Cohen (2000)

Colloquium Mathematicae

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Let a, b, c be relatively prime positive integers such that $a^{2} + b^{2} = c^{2}$ . Jeśmanowicz conjectured in 1956 that for any given positive integer n the only solution of ${(a n)}^{x} + {(b n)}^{y} = {(c n)}^{z}$ in positive integers is x=y=z=2. If n=1, then, equivalently, the equation ${(u^{2} - v^{2})}^{x} + {(2 u v)}^{y} = {(u^{2} + v^{2})}^{z}$ , for integers u>v>0, has only the solution x=y=z=2. We prove that this is the case when one of u, v has no prime factor of the form 4l+1 and certain congruence and inequality conditions on u, v are satisfied.

On integers not of the form n - φ (n)

J. Browkin, A. Schinzel (1995)

Colloquium Mathematicae

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W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^{k} \cdot 509203$ (k = 1, 2,...) is of the form n - φ(n).

A note on Jeśmanowicz' conjecture

Maohua Le (1996)

Colloquium Mathematicae

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