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Sums of Primes and Quadratic Linear Recurrence Sequences
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作者 Artūras DUBICKAS 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第12期2251-2260,共10页
Let u be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on u in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expre... Let u be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on u in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expressible by the sum of a prime number and an element of u has a positive lower density. This criterion is then checked for some second order linear recurrence sequences. It follows, for instance, that the set of positive integers of the form p + [(2 + √3)n], where p is a prime number and n is a positive integer, has a positive lower density. This generalizes a recent result of Enoch Lee. In passing, we show that the periods of linear recurrence sequences of order m modulo a prime number p cannot be "too small" for most prime numbers p. 展开更多
关键词 Romanoff's theorem prime number linear recurrence distribution modulo m asymptotic density
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On a Variant of Giuga Numbers
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作者 Jos María GRAU Florian LUCA Antonio M. OLLER-MARCN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第4期653-660,共8页
In this paper, we characterize the odd positive integers n satisfying the congruence ∑j=1^n-1 j n-1/2 We show that the set of such positive integers has an asymptotic densitywhich turns out to be slightly larger than... In this paper, we characterize the odd positive integers n satisfying the congruence ∑j=1^n-1 j n-1/2 We show that the set of such positive integers has an asymptotic densitywhich turns out to be slightly larger than 3/8. 展开更多
关键词 CONGRUENCE Giuga numbers asymptotic density
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