Diophantine equations with products of consecutive values of a quadratic polynomial
Abstract
Let a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for the function π(x) and some results concerning arithmetic progressions of prime numbers, we study the Diophantine equation∏k=1n(ak2+bk+c)=dyl,gcd(a,b,c)=1,l⩾2, where ax2+bx+c is an irreducible quadratic polynomial. We provide a computable sharp upper bound to n. Using this bound, we entirely prove some conjectures due to Amdeberhan, Medina and Moll (2008)...
Paper Details
Title
Diophantine equations with products of consecutive values of a quadratic polynomial
Published Date
Oct 1, 2011
Journal
Volume
131
Issue
10
Pages
1840 - 1851
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