Binomial coefficients whose products are perfect kth powers

Basil Gordon, Daihachiro Sato and Ernst Gabor Straus

Vol. 118 (1985), No. 2, 393–400

DOI: 10.2140/pjm.1985.118.393

Abstract

A P_k-set is a finite set of positions in Pascal’s triangle which, when translated anywhere within the triangle, covers entries whose product is a perfect k-th power. A characterization of such sets is obtained, and the minimum cardinality f(k) of all P_k-sets is determined.

Mathematical Subject Classification 2000

Primary: 05A10

Secondary: 11B65

Milestones

Received: 10 October 1984

Published: 1 June 1985