Prime Fermat numbers and maximum determinant matrix conjecture
نویسندگان
چکیده
منابع مشابه
Distribution of generalized Fermat prime numbers
Numbers of the form Fb,n = b 2n+1 are called Generalized Fermat Numbers (GFN). A computational method for testing the probable primality of a GFN is described which is as fast as testing a number of the form 2m−1. The theoretical distributions of GFN primes, for fixed n, are derived and compared to the actual distributions. The predictions are surprisingly accurate and can be used to support Ba...
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The French mathematician Pierre de Fermat (1601–1665) was a veritable giant of number theory whose discoveries, and especially, whose conjectures and unproven assertions, kept mathematicians hard at work for several centuries that followed. Indeed, the first two issues of this magazine both featured his work: the first issue reviewed a book ([1]) on the history of what is known as “Fermat’s Las...
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The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
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Fn+1 = (Fn − 1) + 1, n ≥ 0 and are pairwise coprime. It is conjectured that Fn are always square-free and that, beyond F4, they are never prime. The latter would imply that there are exactly 31 regular polygons with an odd number Gm of sides that can be constructed by straightedge and compass [2]. The values G1, G2, . . ., G31 encompass all divisors of 232−1 except unity [3]. Let G0 = 1. If we ...
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In this paper, using permutation matrices or symmetric matrices, necessary and sufficient conditions are given for a generalized matrix function to be the determinant or the permanent. We prove that a generalized matrix function is the determinant or the permanent if and only if it preserves the product of symmetric permutation matrices. Also we show that a generalized matrix function is the de...
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ژورنال
عنوان ژورنال: Информационно-управляющие системы
سال: 2020
ISSN: 2541-8610,1684-8853
DOI: 10.31799/1684-8853-2020-2-2-9