On integers expressible as a sum of two powers, II
نویسندگان
چکیده
منابع مشابه
#a55 Integers 13 (2013) on the Least Primitive Root Expressible as a Sum of Two Squares
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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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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Let k 4 be an integer. We find all integers of the form by where l 2 and the greatest prime factor of b is at most k (i.e. nearly a perfect power) such that they are also products of k consecutive integers with two terms omitted.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1967
ISSN: 0386-2194
DOI: 10.3792/pja/1195521558