Jeremy A. Rouse

activity

20072023

most citedGalois theory of iterated endomorphisms

44 citations · 123 across the 26 of their papers we have counts for

collaborators

Showing 2012 · math.NTShow all

4 papers · 2 filters

math.NT2012★ 1 cited

Divisibility properties of the Fibonacci entry point

Paul Cubre, Jeremy Rouse

For a prime $p$ , let $Z (p)$ be the smallest positive integer $n$ so that $p$ divides $F_{n}$ , the $n$ th term in the Fibonacci sequence. Paul Bruckman and Peter Anderson conjectured…

math.NT2012★ 3 cited

Solutions of the cubic Fermat equation in quadratic fields

Marvin Jones, Jeremy Rouse

We give necessary and sufficient conditions on a squarefree integer $d$ for there to be non-trivial solutions to $x^{3} + y^{3} = z^{3}$ in $\Q(\sqrt{d})$, conditional on the Birch…

math.NT2012★ 3 cited

On the existence of large degree Galois representations for fields of small discriminant

Jeremy Rouse, Frank Thorne

Let $L / K$ be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of $Gal (L / K)$ , the sharpe…

math.NT2012

A 60,000 digit prime number of the form $x^{2} + x + 41$

Justin DeBenedetto, Jeremy Rouse

Motivated by Euler's observation that the polynomial $x^{2} + x + 41$ takes on prime values for $0 \leq x \leq 39$ , we search for large values of $x$ for which $N = x^{2} + x + 41$ …

Divisibility properties of the Fibonacci entry point

Solutions of the cubic Fermat equation in quadratic fields

On the existence of large degree Galois representations for fields of small discriminant

A 60,000 digit prime number of the form x2+x+41

A 60,000 digit prime number of the form $x^{2} + x + 41$