57 citations · 69 across the 6 of their papers we have counts for
8 papers
Using Fibonacci factors to create Fibonacci pseudoprimes
Junhyun Lim, Shaunak Mashalkar, Edward F. Schaefer
Carmichael showed for sufficiently large , that has at least one prime divisor that is . For a given , we will show that a product of distinct o…
Elliptic curves with Galois-stable cyclic subgroups of order 4
Carl Pomerance, Edward F. Schaefer
Infinitely many elliptic curves over have a Galois-stable cyclic subgroup of order 4. Such subgroups come in pairs, which intersect in their subgroups of order 2. Let $N_…
Computing a Selmer group of a Jacobian using functions on the curve
Edward F. Schaefer
In general, algorithms for computing the Selmer group of the Jacobian of a curve have relied on either homogeneous spaces or functions on the curve. We present a theoretical analys…
Class groups and Selmer groups
Edward F. Schaefer
It is often the case that a Selmer group of an abelian variety and a group related to an ideal class group can both be naturally embedded into the same cohomology group. One hopes…
The distance from a point to its opposite along the surface of a box
S. Michael Miller, Edward F. Schaefer
Given a point (the "spider") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the "fly" - the reflection of the spider acro…
The yoga of the Cassels-Tate pairing
Tom Fisher, Edward F. Schaefer, Michael Stoll
Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels-Tate pairing. In this article, we prove that the two pairin…
Twists of X(7) and primitive solutions to x^2+y^3=z^7
Bjorn Poonen, Edward F. Schaefer, Michael Stoll
We find the primitive integer solutions to x^2+y^3=z^7. A nonabelian descent argument involving the simple group of order 168 reduces the problem to the determination of the set of…
Cycles of Quadratic Polynomials and Rational Points on a Genus-Two Curve
E. V. Flynn, Bjorn Poonen, Edward F. Schaefer
It has been conjectured that for sufficiently large, there are no quadratic polynomials in with rational periodic points of period . Morton proved there were no…