John Greene

activity

20152021

collaborators

4 papers

math.NT2021

Using Fibonacci factors to create Fibonacci pseudoprimes

Junhyun Lim, Shaunak Mashalkar, Edward F. Schaefer

Carmichael showed for sufficiently large $L$ , that $F_{L}$ has at least one prime divisor that is $\pm 1 (mod L)$ . For a given $F_{L}$ , we will show that a product of distinct o…

math.CO2020

Nullities for a class of skew-symmetric Toeplitz band matrices

Ron Evans, John Greene, Mark Van Veen

For all $n > k \geq 1$ , we give formulas for the nullity $N (n, k)$ of the $n \times n$ skew-symmetric Toeplitz band matrix whose first $k$ superdiagonals have all entries $1$ and who…

math.NT2016

Some mixed character sum identities of Katz II

Ron Evans, John Greene

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p > 3. His…

math.NT2015

A quadratic hypergeometric 2F1 transformation over finite fields

Ron Evans, John Greene

In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric 2F1 functions over a finite field F_q. We prove this conjecture and give…