On Elements of Sumsets with Many Prime Factors
نویسندگان
چکیده
منابع مشابه
Congruent numbers with many prime factors.
Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite ...
متن کاملIntegral Domains Having Nonzero Elements with Infinitely Many Prime Divisors
In a factorial domain every nonzero element has only finitely many prime divisors. We study integral domains having nonzero elements with infinitely many prime divisors. Let D be an integral domain. It is well known that if D is a UFD then every nonzero element has only finitely many prime divisors (see e.g. [G]). This is also true if D is a Noetherian domain, or more generally, if D satisfies ...
متن کاملClassification theorems for sumsets modulo a prime
Let Zp be the finite field of prime order p and A be a subsequence of Zp. We prove several classification results about the following questions: (1) When can one represent zero as a sum of some elements of A ? (2) When can one represent every element of Zp as a sum of some elements of A ? (3) When can one represent every element of Zp as a sum of l elements of A ?
متن کاملCounting (k,l)-sumsets in groups of prime order
A subset A of a group G is called (k, l)-sumset, if A = kB−lB for some B ⊆ G, where kB − lB = {x1 + · · · + xk − xk+1 − · · · − xk+l : x1, . . . , xk+l ∈ B}. Upper and lower bounds for the number (k, l)-sumsets in groups of prime order are provided.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1993
ISSN: 0022-314X
DOI: 10.1006/jnth.1993.1038