On distinct unit fractions whose sum equals 1
نویسندگان
چکیده
منابع مشابه
On partitions into squares of distinct integers whose reciprocals sum to 1
In 1963, Graham [1] proved that all integers greater than 77 (but not 77 itself) can be partitioned into distinct positive integers whose reciprocals sum to 1. He further conjectured [2, Section D11] that for any sufficiently large integer, it can be partitioned into squares of distinct positive integers whose reciprocals sum to 1. In this study, we establish the exact bound for existence of su...
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We shall consider the representation of numbers as the sum of distinct unit fractions ; in particular we will answer two questions recently raised by Herbert S . Wilf . A sequence of positive integers S= n 1 , n2 , } with ni < ,n 2< is an R-basis if every positive integer is the sum of distinct reciprocals of finitely many integers of S . In Research Problem 6 [1, p. 457], Herbert S. Wilf raise...
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We first prove two results which both imply that for any sequence B of asymptotic density zero there exists an infinite sequence A such that the sum of any number of distinct elements of A does not belong to B. Then, for any ε > 0, we construct an infinite sequence of positive integers A = {a1 < a2 < a3 < . . . } satisfying an < K(ε)(1 + ε)n for each n ∈ N such that no sum of some distinct elem...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1973
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90136-2