Egyptian fractions with restrictions

Abstract

Let T o (k) denote the number of solutions ofthe inverse sum of all elements s j > 1 in S(p 1 , p 2 , . . ., p t ) is more than 1.In this paper we study T o (k) and T k (p 1 , . . ., p t ).Three of our results are:2) if the inverse sum of all elements s j > 1 in S(p 1 , p 2 , . . ., p t ) is more than 1, then T k (p 1 , . . ., p t ) = 0 for infinitely many k and the set of these k is the union of finitely many arithmetic progressions;3) there exists two constants k 0 = k 0 (p 1 , . . ., p t ) > 1 and c = c(p 1 , . . ., p t ) > 1 such that for any k > k 0 we have either T k (p 1 , . . ., p t ) = 0 or T k (p 1 , . . ., p t ) > c k .Motivated by this, let T o (k) denote the number of solutions of k i=1

Locations

• Acta Arithmetica - View - PDF
• arXiv (Cornell University) - View - PDF
• DataCite API - View