Powers from products of consecutive terms in arithmetic progression
MA Bennett, N Bruin, K Györy, L Hajdu - Proceedings of the London …, 2006 - cambridge.org
MA Bennett, N Bruin, K Györy, L Hajdu
Proceedings of the London Mathematical Society, 2006•cambridge.orgWe show that if, we obtain the more precise conclusion that there are, in fact, no such
progressions. Our proofs exploit the modularity of Galois representations corresponding to
certain Frey curves, together with a variety of results, classical and modern, on solvability of
ternary Diophantine equations. As a straightforward corollary of our work, we sharpen and
generalize a theorem of Sander on rational points on superelliptic curves.
progressions. Our proofs exploit the modularity of Galois representations corresponding to
certain Frey curves, together with a variety of results, classical and modern, on solvability of
ternary Diophantine equations. As a straightforward corollary of our work, we sharpen and
generalize a theorem of Sander on rational points on superelliptic curves.
We show that if , we obtain the more precise conclusion that there are, in fact, no such progressions. Our proofs exploit the modularity of Galois representations corresponding to certain Frey curves, together with a variety of results, classical and modern, on solvability of ternary Diophantine equations. As a straightforward corollary of our work, we sharpen and generalize a theorem of Sander on rational points on superelliptic curves.
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