Numbers having $m$ small $m$th roots mod $p$
نویسندگان
چکیده
منابع مشابه
NUMBERS HAVING m SMALL rath ROOTS mod p
Here are two typical results about the numbers mentioned in the title: If p is a prime such that p = 1 (mod 6) and p > 67, then there are exactly six numbers mod p , each of which has six sixth roots less than 2yf}p in absolute value. If p is a prime such that p = 1 (mod 8), then there is at least one number mod p which has eight eighth roots less than p3/4 in absolute value.
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Let m be a positive integer and suppose that p is an odd prime with p ≡ 1 mod m. Suppose that a ∈ (Z/pZ)∗ and consider the polynomial xm − a. If this polynomial has any roots in (Z/pZ)∗, where the coset representatives for Z/pZ are taken to be all integers u with |u| < p/2, then these roots will form a coset of the multiplicative subgroup μm of (Z/pZ)∗ consisting of the mth roots of unity mod p...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1993
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1993-1189522-0