Add to ORKGErdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power. That is, the equation x(x+ 1) · · · (x+ (m − 1)) = yn has no solutions in positive integers x, y,m, n with m,n> 1. A natural problem is to study the equation x(x+ 1)(x+ 2)...(x+ (m − 1)) + r = yn (1
AbstractAll solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are de...
In this note, we study another equation which visually resembles the Pythagorean equation and which...
For each integer n≥1 we consider the unique polynomials P,Q∈Q[x] of smallest degree n that are solut...
We shall consider the following problem: Could a product of some consecutive integers be a power of ...
A celebrated theorem of Erdős and Selfridge [5] asserts that a product of consecutive nonzero integ...
Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In ...
AbstractIn this paper it has been proved that if q is an odd prime, q≢7 (mod 8), n is an odd integer...
THEOREM. The equation of the title has no solutions in positive integers x, y for any value of the p...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
This paper investigates and determines the solutions for the Diophantine equation x2 + 4.7b = y2r, w...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
AbstractAll solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are de...
In this note, we study another equation which visually resembles the Pythagorean equation and which...
For each integer n≥1 we consider the unique polynomials P,Q∈Q[x] of smallest degree n that are solut...
We shall consider the following problem: Could a product of some consecutive integers be a power of ...
A celebrated theorem of Erdős and Selfridge [5] asserts that a product of consecutive nonzero integ...
Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In ...
AbstractIn this paper it has been proved that if q is an odd prime, q≢7 (mod 8), n is an odd integer...
THEOREM. The equation of the title has no solutions in positive integers x, y for any value of the p...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
This paper investigates and determines the solutions for the Diophantine equation x2 + 4.7b = y2r, w...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
AbstractAll solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are de...
In this note, we study another equation which visually resembles the Pythagorean equation and which...
For each integer n≥1 we consider the unique polynomials P,Q∈Q[x] of smallest degree n that are solut...