The Lowest-Degree Polynomial with Nonnegative Coefficients Divisible by the $n$-th Cyclotomic Polynomial
نویسندگان
چکیده
منابع مشابه
The Lowest-Degree Polynomial with Nonnegative Coefficients Divisible by the n-th Cyclotomic Polynomial
We pose the question of determining the lowest-degree polynomial with nonnegative coefficients divisible by the n-th cyclotomic polynomial Φn(x). We show this polynomial is 1+x+· · ·+x where p is the smallest prime dividing n whenever 2/p > 1/q1+· · ·+1/qk, where q1, . . . , qk are the other (distinct) primes besides p dividing n. Determining the lowestdegree polynomial with nonnegative coeffic...
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For a given positive integer m and an algebraic number field K necessary and sufficient conditions for the mth cyclotomic polynomial to have K-integral solutions modulo a given integer of K are given. Among applications thereof are: that the solvability of the cyclotomic polynomial mod an integer yields information about the class number of related number fields; and about representation of int...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2755