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On a set of asymptotic densities

Pavel JahodaMonika Jahodová — 2008

Acta Mathematica Universitatis Ostraviensis

Let = { p 1 , p 2 , , p i , } be the set of prime numbers (or more generally a set of pairwise co-prime elements). Let us denote A p a , b = { p a n + b m n { 0 } ; m , p does not divide m } , where a , b { 0 } . Then for arbitrary finite set B , B holds d p i B A p i a i , b i = p i B d A p i a i , b i , and d A p i a i , b i = 1 p i b i 1 - 1 p i 1 - 1 p i a i . If we denote A = 1 p b 1 - 1 p 1 - 1 p a p , a , b { 0 } , where is the set of all prime numbers, then for closure of set A holds cl A = A B { 0 , 1 } , where B = 1 p b 1 - 1 p p , b { 0 } .

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