1964/03/01 by Ronald Graham · 4 citations
Mathematics · #Analytic Number Theory Research #Combinatorics #Discrete mathematics #History and Theory of Mathematics #Integer (computer science) #Mathematics #Mathematics and Applications #Pure mathematics #Rational number
paper · pdf · doi:10.2140/pjm.1964.14.85
openalex publication_date 1964/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06
Introduction* It has long been known that every positive rational number can be represented as a of reciprocals of distinct positive integers (the first proof having been given by Leonardo Pisano [6] in 1202). It is the purpose of this paper to characterize cf. Theorem 4) those rational numbers which can be written as sums of reciprocals of distinct nth. powers of integers, where n is an arbitrary (fixed) positive integer and finite sum denotes a with a number of summands. It will follow, for example, that p\q is the of reciprocals of distinct squares if and only if