Sur l'équation $x^z - y^t =1$, où $|x - y| = 1$
نویسندگان
چکیده
منابع مشابه
A Note on Twists of (y^2=x^3+1)
‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with ...
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in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), and of the generic rank at least two and at least three as cubic twists of (e_1). previous work, in the category of mordell curves with trivial torsion groups, has found infinitely many elliptic curves with rank at least seven as sextic tw...
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There is no restriction in assuming that y > x in (1) and thus we have m > n. This equation asks for integers having all their digits equal to one with respect to two distinct bases and we still do not know whether or not it has finitely many solutions. Even if we fix one of the four variables, it remains an open question to prove that (1) has finitely many solutions. However, when either the b...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1956
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-3-1-5-6