additive number theory

短语

释义与例句

n.
  1. 1.

    The subfield of number theory concerning the behaviour of sumsets (integer sets added to each other elementwise).

    不可数 数学

    Abstractly, additive number theory includes the study of abelian groups and commutative semigroups with an addition operation.

    Two principal objects of study in additive number theory are the sumset A#43;B#61;#92;#123;a#43;b#58;a#92;inA,b#92;inB#92;#125; of two subsets A and B of elements from an abelian group G, and the h-fold sumset of A, hA#61;#92;underset#123;h#125;#123;#92;underbrace#123;A#43;#92;cdots#43;A

    Additive number theory has close ties to combinatorial number theory and the geometry of numbers.

    1966 [Macmillan], W. E. Deskins, Abstract Algebra, 1995, Dover, page 152, One of the famous theorems of additive number theory states that each positive integer is expressible in at least one way as the sum of the squares of not more than four positive integers.