AbstractCertain diophantine equations of the form x2 − Dy2 = nz2 are solved parametrically. In particular, a case where D = −11 and n = 3 is studied in detail. Several examples show the utilization of quadratic forms in equations of this kind
In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combine ...
AbstractLet D be a positive integer with 2 ∤ D, and let p be an odd prime with p ∤ lD. Further let N...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
AbstractCertain diophantine equations of the form x2 − Dy2 = nz2 are solved parametrically. In parti...
In this note parametric solutions of certain diophantine equations are given. The method of obtainin...
In this note parametric solutions of certain diophantine equations are given. The method of obtainin...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractAll Diophantine equations ax2 + by2 + cz2 = 1 + dxyz, with a, b, c, d ∈ N and a|d, b|d, c|d,...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
AbstractThe diophantine equation of the title has been solved by Ljunggren, by indirect use of the p...
In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combin...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
The Diophantine equation ax+py = z2 where p is prime is widely studied by many mathematicians. Solv...
AbstractWe show that the equations x10 + y10 = z2 and x10 - y10 = z2 have no nontrivial integral sol...
In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combine ...
AbstractLet D be a positive integer with 2 ∤ D, and let p be an odd prime with p ∤ lD. Further let N...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
AbstractCertain diophantine equations of the form x2 − Dy2 = nz2 are solved parametrically. In parti...
In this note parametric solutions of certain diophantine equations are given. The method of obtainin...
In this note parametric solutions of certain diophantine equations are given. The method of obtainin...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractAll Diophantine equations ax2 + by2 + cz2 = 1 + dxyz, with a, b, c, d ∈ N and a|d, b|d, c|d,...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
AbstractThe diophantine equation of the title has been solved by Ljunggren, by indirect use of the p...
In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combin...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
The Diophantine equation ax+py = z2 where p is prime is widely studied by many mathematicians. Solv...
AbstractWe show that the equations x10 + y10 = z2 and x10 - y10 = z2 have no nontrivial integral sol...
In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combine ...
AbstractLet D be a positive integer with 2 ∤ D, and let p be an odd prime with p ∤ lD. Further let N...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
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