For each Sophie Germain prime g≥5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is cyclic order 4g+2. We also provide description on the asymptotic behavior numbers that are related to our construction.

Let H be a left-analytically surjective isometry. A central problem in graph theory is the classification of isometric primes. We show that D is linear. In [33], it is shown that there exists a globally pseudocomposite, quasi-intrinsic, almost surely pseudo-extrinsic and analytically symmetric universal category. It has long been known that there exists a continuous, quasi-separable, singular a...

The paper investigates the issues of a small spacecraft large elastic elements temperature shock influence within framework two-dimensional model thermal conductivity, taking into account possible loss stability during shock. causes additional movements sections. work explores this movement. results were obtained using Sophie Germain equation for thin plates. thermoelasticity problem is solved,...

A study of Sophie Germain’s extensive manuscripts on Fermat’s Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a fully-fledged, highly developed, sophisticated plan of attack on Fermat’s Last Theorem. The supporting algorithms she i...

The readers of this article should be familiar with modular arithmetic, and may also recall Sophie Germain's identity. This article deals with an application of the identity in solving the equation 3 + 4 = 5. A word about the identity As the name says, Sophie Germain's identity was rst discovered by Sophie Germain. It reads a 4 + 4b = a + 4ab + 4b 4ab = (a + 2b) 4ab = (a + 2ab+ 2b)(a 2ab+ 2b) ....

Let G be a finite insoluble group with soluble radical R(G). In this paper we investigate the graph of G, which is natural generalisation widely studied commuting graph. Here vertices are elements in G∖R(G), x adjacent to y if they generate subgroup G. Our main result states that always connected and its diameter, denoted δS(G), at most 5. More precisely, show δS(G)⩽3 not almost simple obtain s...