Some number theoretic results

Paul Erdős and Ernst Gabor Straus

Vol. 36 (1971), No. 3, 635–646

DOI: 10.2140/pjm.1971.36.635

Abstract

The paper first establishes the order of magnitude of maximal sets, S, of residues ( mod p) so that the sums of different numbers of elements are distinct.

In the second part irrationalities of Lambert Series of the form ∑ f(n)∕α₁⋯a_n are obtained where f(n) = d(n),σ(n) or φ(n) and the a_i are integers, a_i ≧ 2, which satisfy suitable growth conditions.

Mathematical Subject Classification

Primary: 10.55

Milestones

Received: 27 May 1970

Published: 1 March 1971