A note on the Diophantine equation
Diophantine equations and class numbers of real quadratic fields
An application of a lower bound for linear forms in two logarithms to the Terai-Jeśmanowicz conjecture
Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.
Diophantine equations and class number of imaginary quadratic fields
Let A, D, K, k ∈ ℕ with D square free and 2 ∤ k,B = 1,2 or 4 and , and let denote the class number of the imaginary quadratic field . In this paper, we give the all-positive integer solutions of the Diophantine equation Ax² + μ₁B = K((Ay² + μ₂B)/K)ⁿ, 2 ∤ n, n > 1 and we prove that if D > 1, then , where D, and n satisfy , x ∈ ℕ, 2 ∤ n, n > 1. The results are valuable for the realization of quadratic field cryptosystem.
The simultaneous Pell equations y²-Dz² = 1 and x²-2Dz² = 1
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