SOLVING n(n + d) ⋯ (n + (k - 1)d) = by2WITH P(b) ≤ Ck-Reference-Cited by-同舟云学术

SOLVING n(n + d) ⋯ (n + (k - 1)d) = by2WITH P(b) ≤ Ck

Published:2012-02 Issue:01 Volume:08 Page:161-173
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

FILASETA M.¹,LAISHRAM S.²,SARADHA N.³

Affiliation:

1. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

2. Stat-Math Unit, Indian Statistical Institute, New Delhi 110016, India

3. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

Abstract

We examine the problem of determining the solutions to the Diophantine equation [Formula: see text] where d is fixed and the largest prime divisor of b is no more than Ck. Here, C is fixed but arbitrary. Under some rather minor conditions, it is shown that there are finitely many solutions that can be effectively computed. Some new, largely combinatorial, ideas are introduced into the general theory to handle the case of arbitrary C as considered here.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042112500091

Reference18 articles.

1. Transcendental Number Theory

2. POWERS FROM PRODUCTS OF CONSECUTIVE TERMS IN ARITHMETIC PROGRESSION

3. Solving Thue Equations of High Degree

4. Multiplicative Number Theory

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