Differences between perfect powers: The Lebesgue-Nagell equation
نویسندگان
چکیده
We develop a variety of new techniques to treat Diophantine equations the shape x 2 + D = y n x^2+D =y^n , based upon bounds for linear forms in alttext="p"> p encoding="application/x-tex">p -adic and complex logarithms, modularity Galois representations attached Frey-Hellegouarch elliptic curves, machinery from approximation. use these explicitly determine set all coprime integers alttext="x"> encoding="application/x-tex">x alttext="y"> encoding="application/x-tex">y alttext="n greater-than-or-equal-to 3"> ≥ 3 encoding="application/x-tex">n \geq 3 with property that alttext="y n Baseline greater-than x squared"> > encoding="application/x-tex">y^n > x^2 minus −<!-- − encoding="application/x-tex">x^2-y^n has no prime divisor exceeding alttext="11"> 11 encoding="application/x-tex">11 .
منابع مشابه
Lebesgue–nagell Equation
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2022
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8734