On numbers expressible as a weighted sum of powers
نویسندگان
چکیده
منابع مشابه
Perfect Powers Expressible as Sums of Two Cubes
Let n ≥ 3. This paper is concerned with the equation a3 + b3 = cn, which we attack using a combination of the modular approach (via Frey curves and Galois representations) with obstructions to the solutions that are of Brauer–Manin type. We shall show that there are no solutions in coprime, non-zero integers a, b, c, for a set of prime exponents n having Dirichlet density 28219 44928 ≈ 0.628, a...
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For a positive integer n, a -root modulo n is an integer q coprime to n which has maximal order in (Z /n Z)⇤. We establish upper bounds for s⇤(n), the least -root modulo n which is expressible as a sum of two squares, in particular proving that for " > 0, and n large enough there always exists a -root q modulo n in the range 1 q n 2+" such that q is a sum of two squares.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1968
ISSN: 0386-2194
DOI: 10.3792/pja/1195520976