Almost primality of group orders of elliptic curves defined over small finite fields.
Koblitz, Neal (2001)
Experimental Mathematics
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Koblitz, Neal (2001)
Experimental Mathematics
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R. Hall (1971)
Acta Arithmetica
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Dubner, Harvey (2002)
Journal of Integer Sequences [electronic only]
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William J. Ellison (1973-1974)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Fumiyuki Momose (1995)
Compositio Mathematica
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Jean-Marie De Koninck, Jason Pierre Sweeney (2001)
Colloquium Mathematicae
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The main objective of this paper is to analyze the unimodal character of the frequency function of the largest prime factor. To do that, let P(n) stand for the largest prime factor of n. Then define f(x,p): = #{n ≤ x | P(n) = p}. If f(x,p) is considered as a function of p, for 2 ≤ p ≤ x, the primes in the interval [2,x] belong to three intervals I₁(x) = [2,v(x)], I₂(x) = ]v(x),w(x)[ and I₃(x) = [w(x),x], with v(x) < w(x), such that f(x,p) increases for p ∈ I₁(x), reaches its maximum...
Andrzej Rotkiewicz (2005)
Acta Mathematica Universitatis Ostraviensis
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We use the properties of -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
Lindsey Reinholz, Blair K. Spearman, Qiduan Yang (2015)
Colloquium Mathematicae
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We give infinitely many new families of non-congruent numbers where the first prime factor of each number is of the form 8k+1 and the rest of the prime factors have the form 8k+3. Products of elements in each family are shown to be non-congruent.
Granville, Andrew, Selfridge, J. L. (2002)
The Electronic Journal of Combinatorics [electronic only]
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Lawrence Washington (1975)
Acta Arithmetica
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