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The normal number of prime factors of f a ( n ) FILIP SAIDAK
Assuming a quasi-generalized Riemann Hypothesis (6) for certain Dedekind zeta functions, we prove the following theorem: If a ≥ 2 is a square-free integer, then for the exponent function f a (n)Expand
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ZHOU ’ S THEORY OF CONSTRUCTING IDENTITIES
We give a new simple proof of Chizhong Zhou’s method of constructing identities for linear recurrence sequences. We show how Zhou’s theorem can be used to prove a wide variety of identities forExpand
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On the modulus of the Riemann zeta function in the critical strip
For the Riemann zeta function C( s ), defined for complex s = cr+it, we write a = ^ + A, and we study the horizontal behaviour of |C( S)| in the critical strip |A| |CQ+A +І I ) for 0 < A < T-, 27T +Expand
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Square-free values of the Carmichael function
We obtain an asymptotic formula for the number of square-free values among p−1, for primes p⩽x, and we apply it to derive the following asymptotic formula for L(x), the number of square-free valuesExpand
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A note on the maximal coefficients of squares of Newman polynomials
Abstract In a recent paper [G. Yu, An upper bound for B 2 [ g ] sets, J. Number Theory 122 (1) (2007) 211–220] Gang Yu stated the following conjecture: Let { p i } i = 1 ∞ be an arbitrary sequence ofExpand
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Non-Abelian Generalizations of the Erdős-Kac Theorem
Abstract Let $a$ be a natural number greater than 1. Let ${{f}_{a}}\left( n \right)$ be the order of $a\,\bmod \,n$ . Denote by $\omega \left( n \right)$ the number of distinct prime factors of $n$ .Expand
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On Goldbach's Conjecture for Integer Polynomials
  • F. Saidak
  • Mathematics, Computer Science
  • Am. Math. Mon.
  • 1 June 2006
TLDR
We give a short proof of the fact that every monic polynomial f (x) in Z[x] can be written as a sum of two irreducible monics g(x) and h(x). Expand
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Descartes Numbers
We call n a Descartes number if n is odd and n = km for two integers k,m > 1 such that σ(k)(m + 1) = 2n, where σ is the sum of divisors function. In this paper, we show that the only cube-freeExpand
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Horizontal Monotonicity of the Modulus of the Riemann Zeta Function and Related Functions
As usual let s = �+it. For any fixed value t = t0 with |t0| ≥ 8, and for � ≤ 0, we show that |�(s)| is strictly monotone decreasing in �,
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Riemann and his zeta function
An exposition is given, partly historical and partly mathematical, of the Riemann zeta function � ( s ) and the associated Riemann hypothesis. Using techniques similar to those of Riemann, it isExpand
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