Graham Everest 1957-2010

Rational Points on Elliptic Curves Graham Everest, Jonathan Reynolds and Shaun Stevens

We consider the structure of rational points on elliptic curves in Weierstrass form. Let x(P ) = AP /B P denote the xcoordinate of the rational point P then we consider when BP can be a prime power. Using Faltings’ Theorem we show that for a fixed power greater than 1, there are only finitely many rational points with this property. Where descent via an isogeny is possible we show, with no rest...

Primitive Divisors on Twists of the Fermat Cubic Graham Everest, Patrick Ingram and Shaun Stevens

We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u + v = m, with m cube-free, all the terms beyond the first have a primitive divisor. 1. Statement of Main Theorem Let C denote a twist of the Fermat cubic, C : U + V 3 = mW 3 (1) with m a non-zero rational number. If K denotes any field of characteristic zero, the set C(K) of projective K-rational points satisfy...

The Uniform Primality Conjecture for the Twisted Fermat Cubic Graham Everest, Ouamporn Phuksuwan and Shaun Stevens

On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. We prove that the number of prime terms in the sequence is uniformly bounded. When the rational point is the image of another rational point under a certain 3-isogeny, all terms beyond the first fail to be primes.

Graham Lusk *

Caudwell xtreme Everest expedition.

The Caudwell Xtreme Everest (CXE) expedition involved the detailed study of 222 subjects ascending to 5300 m or higher during the first half of 2007. Following baseline measurements at sea level, 198 trekker-subjects trekked to Everest Base Camp (EBC) following an identical ascent profile. An additional group of 24 investigator-subjects followed a similar ascent to EBC and remained there for th...