Displaying similar documents to “The distribution of group structures on elliptic curves over finite prime fields.”

On the unimodal character of the frequency function of the largest prime factor

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...

On pseudoprimes having special forms and a solution of K. Szymiczek’s problem

Andrzej Rotkiewicz (2005)

Acta Mathematica Universitatis Ostraviensis

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We use the properties of p -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.

On the prime factors of non-congruent numbers

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.