Add to ORKGA celebrated theorem of Erdős and Selfridge [5] asserts that a product of consecutive nonzero integers can never be a perfect power. More generally, the techniques of [5] have been extended and refined by Győry [6] and Saradha [9] to prove that the Diophantine equation n(n+ 1)(n+ 2) · · · (n+ k − 1) = byl (1
Abstract. In this paper, we present a new technique for determining all perfect powers in so-called ...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
Erdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power....
Let n, d, k ≥ 2, b, y and l ≥ 3 be positive integers with the greatest prime factor of b not exceedi...
For all integers a, b, c, assuming the true abc n−conjecture in the case n = 5, there are finitely m...
Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In ...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
Article dans revue scientifique avec comité de lecture.We study a generalized version of a theorem o...
Perfect powers in products of terms in an arithmetical progression III by T. N. Shorey (Bombay) and ...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
On arithmetic progressions of equal lengths and equal products of terms by Ajai Choudhry (Beirut) Th...
We shall consider the following problem: Could a product of some consecutive integers be a power of ...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
Abstract. In this paper, we present a new technique for determining all perfect powers in so-called ...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
Erdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power....
Let n, d, k ≥ 2, b, y and l ≥ 3 be positive integers with the greatest prime factor of b not exceedi...
For all integers a, b, c, assuming the true abc n−conjecture in the case n = 5, there are finitely m...
Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In ...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
Article dans revue scientifique avec comité de lecture.We study a generalized version of a theorem o...
Perfect powers in products of terms in an arithmetical progression III by T. N. Shorey (Bombay) and ...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
On arithmetic progressions of equal lengths and equal products of terms by Ajai Choudhry (Beirut) Th...
We shall consider the following problem: Could a product of some consecutive integers be a power of ...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
Abstract. In this paper, we present a new technique for determining all perfect powers in so-called ...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...
If a, b and n are positive integers with b = a and n = 3, then the equation of the title possesses a...