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
A set of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two e...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
AbstractQuestions, partial and complete answers about the diophantine equation ∑i=1k1/xi=1 in distin...
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 A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractLet k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integ...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractThe solution by Barbeau [Expressing one as a sum of distinct reciprocals: comments and a bib...
In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the dioph...
A set of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two e...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
AbstractQuestions, partial and complete answers about the diophantine equation ∑i=1k1/xi=1 in distin...
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 A1, …, Ar, x1, …, xr, and A be known positive integers. Let f(A) be the number of intege...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractLet k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integ...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractThe solution by Barbeau [Expressing one as a sum of distinct reciprocals: comments and a bib...
In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the dioph...
A set of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two e...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
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