Some Remarks on Harmonic Type Matrices

Abstract

In 1915, Theisinger proved that all harmonic numbers are not integers except for the first one. In 1862, Wolstenholme proved that the numerator of the reduced form of the harmonic number Hp−1 is divisible by p2 and the numerator of the reduced form of the generalized harmonic number (Formula presented) is divisible by p for all primes p ≥ 5. In this note, we define harmonic type matrices and our goal is to extend Theisinger’s and Wolstenholme’s results to harmonic type matrices. © 2022, Colgate University. All rights reserved.