Determination of elliptic curves with everywhere good reduction over ℚ(√37)
Développement en fraction continue à l'entier supérieur, idéaux 0-réduits et un problème d'Eisenstein
Diagonal cubic equations
Diagonal cubic equations. II
Diagonal equations of different degrees over p-adic fields
Diagonal forms of prime degree p in a P-adic ring
Dichteschranken für die Lösbarkeit gewisser linearer Gleichungen.
Die abc-Vermutung.
Diophantine Analysis Applied to Virus Structure.
Diophantine approximation involving primes.
Diophantine eaquations of the form ax2 + Db2 = yp.
Diophantine equation for four prime divisors of
In this paper the special diophantine equation with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of .
Diophantine equations after Fermat’s last theorem
These are expository notes that accompany my talk at the 25th Journées Arithmétiques, July 2–6, 2007, Edinburgh, Scotland. I aim to shed light on the following two questions:(i)Given a Diophantine equation, what information can be obtained by following the strategy of Wiles’ proof of Fermat’s Last Theorem?(ii)Is it useful to combine this approach with traditional approaches to Diophantine equations: Diophantine approximation, arithmetic geometry, ...?
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.
Diophantine equations and class numbers of real quadratic fields
Diophantine equations and identities.
Diophantine equations E(x) = P(x) with E exponential, P polynomial
Diophantine equations in cyclotomic fields.
Diophantine equations involving factorials
We study the Diophantine equations and where and are positive integers. We show that the first one holds if and only if or and that the second one holds if and only if .
Diophantine equations of matching games II