2 citations · 3 across the 8 of their papers we have counts for
8 papers
On the special harmonic numbers and modulo
John Blythe Dobson
Building on work of Zhi-Hong Sun, we establish congruences for the special harmonic numbers and modulo , which contain respect…
A matrix variation on Ramus's identity for lacunary sums of binomial coefficients
John Blythe Dobson
We study the well-known lacunary sums of binomial coefficients considered, most notably, by Christian Ramus, and their connection to a special kind of harmonic number associated wi…
Calculations relating to some special Harmonic numbers
John Blythe Dobson
We report on the results of a computer search for primes which divide an Harmonic number with small .
On the Andrews congruence for the Fibonacci quotient
John Blythe Dobson
We show that a congruence discovered by George E. Andrews in 1969 for the Fibonacci quotient directly implies a simpler congruence found by Hugh C. Williams in 1991.
Extended calculations of a special Harmonic number
John Blythe Dobson
The search for values of for which the Harmonic numbers vanish mod , carried to by Schwindt in 1983, is extended here to $p < 149,250…
A characterization of Wilson-Lerch primes
John Blythe Dobson
This note presents criteria in terms of Bernoulli numbers for a number to be simultaneously a Wilson prime and a Lerch prime.
On Eisenstein's formula for the Fermat quotient
John Blythe Dobson
This paper presents some refinements of the representation of the Fermat quotient of base 2 as an alternating series which was discovered by Eisenstein in 1850, including some eval…
On Lerch's formula for the Fermat quotient
John Blythe Dobson
This paper explores some previously-unrecognized consequences of Lerch's 1905 formula for the Fermat quotient, with special attention to the sums which he introduced in this contex…