On some generalizations of the diophantine equation $1^k + 2^k + ... + x^k = y^z$
نویسندگان
چکیده
منابع مشابه
A computational approach for solving y2 =1k + 2k + ... + xk
We present a computational approach for finding all integral solutions of the equation y2 = 1k + 2k + · · ·+xk for even values of k. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we deter...
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= c for some integers a, b, c with ab 6= 0, has only finitely many integer solutions. Stoll & Tichy proved more generally that if a, b, c ∈ Q and ab 6= 0, then for m > n ≥ 3, the above equation has only finitely many integral solutions x, y. Independently, Rakaczki established a more precise finiteness result on this binomial equation and extended this result to more general equations (see Acta...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1984
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-44-2-99-107