AbstractQuestions, partial and complete answers about the diophantine equation ∑i=1k1/xi=1 in distinct positive integers are given when additional requirements are asked on the xi's such as: being large, odd, even or xi∤xj for i≠j. Various combinations of the above conditions are also considered
For each integer n≥1 we consider the unique polynomials P,Q∈Q[x] of smallest degree n that are solut...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
AbstractQuestions, partial and complete answers about the diophantine equation ∑i=1k1/xi=1 in distin...
AbstractIt is shown: (i) there exist distinct odd naturals, the sum of whose reciprocals is equal to...
AbstractFive solutions of the equation ∑i=191xi=1 in distinct odd integers are already known. In thi...
In the present paper we obtained all positive integer solutions of some diophantine equations relate...
AbstractThe solution by Barbeau [Expressing one as a sum of distinct reciprocals: comments and a bib...
AbstractFive solutions of the equation ∑i=191xi=1 in distinct odd integers are already known. In thi...
AbstractIt is shown: (i) there exist distinct odd naturals, the sum of whose reciprocals is equal to...
AbstractLet m and n be positive integers and p any odd prime. In this paper we consider the Diophant...
In this paper we combine theoretical results and computer search to obtain information about the ...
In this paper we combine theoretical results and computer search to obtain information about the ...
AbstractFor given positive integers n and a, let R(n;a) denote the number of positive integer soluti...
Erdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power....
For each integer n≥1 we consider the unique polynomials P,Q∈Q[x] of smallest degree n that are solut...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
AbstractQuestions, partial and complete answers about the diophantine equation ∑i=1k1/xi=1 in distin...
AbstractIt is shown: (i) there exist distinct odd naturals, the sum of whose reciprocals is equal to...
AbstractFive solutions of the equation ∑i=191xi=1 in distinct odd integers are already known. In thi...
In the present paper we obtained all positive integer solutions of some diophantine equations relate...
AbstractThe solution by Barbeau [Expressing one as a sum of distinct reciprocals: comments and a bib...
AbstractFive solutions of the equation ∑i=191xi=1 in distinct odd integers are already known. In thi...
AbstractIt is shown: (i) there exist distinct odd naturals, the sum of whose reciprocals is equal to...
AbstractLet m and n be positive integers and p any odd prime. In this paper we consider the Diophant...
In this paper we combine theoretical results and computer search to obtain information about the ...
In this paper we combine theoretical results and computer search to obtain information about the ...
AbstractFor given positive integers n and a, let R(n;a) denote the number of positive integer soluti...
Erdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power....
For each integer n≥1 we consider the unique polynomials P,Q∈Q[x] of smallest degree n that are solut...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
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