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Title: Power integral points on elliptic curves
Author: Buck, Daniel
ISNI:       0000 0004 5346 5629
Awarding Body: University of East Anglia
Current Institution: University of East Anglia
Date of Award: 2014
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This thesis looks at some of the modern approaches towards the solution of Diophantine equations, and utilizes them to display the nonexistence of perfect powers occurring in certain types of sequences. In particular we look at the denominator divisibility sequences (Bn) formed by Mordell elliptic curves ED : y2 = x3+D. For the curve-point pair (E−2, P), where E−2 : y2 = x3 −2, and P = (3, 5) is a nontorsion point, we prove that no term Bn is a perfect 5th power, and we give the explicit bound p � 137 for any term in the associated elliptic denominator sequence to be a perfect power Bn = Zpn for 1 < n < 113762879. We then look at obtaining upper bounds on p for the seventy-two rank 1 Mordell curves in the range |D| < 200 to possess a pth perfect power. This is done by consideration of the finite number of rational and irrational newforms corresponding to an also finite number of levels of these newforms: in thirty cases we give a bound via examination of both the rational and irrational cases, and for the remaining forty-two cases our bound is merely for the rational case due to computational limitations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available