摘要
In this paper,we prove that when υ ≡0(mod 3),the necessary condition for the existence of cyclic (υ,k,λ) -difference set is that the equation n=x 2+y 2+xy has a nonnegative solution in integers x,y (where n=k-λ ).From this conclusion we obtain that i)there do not exist cyclic (υ,k,λ) -difference set when k-λ≡6 or 10(mod 12);ii)when p ≡1(mod 3)is a prime number,then the equation p=x 2+y 2+xy has a nonnegative solution in integers x,y .
In this paper,we prove that when υ ≡0(mod 3),the necessary condition for the existence of cyclic (υ,k,λ) -difference set is that the equation n=x 2+y 2+xy has a nonnegative solution in integers x,y (where n=k-λ ).From this conclusion we obtain that i)there do not exist cyclic (υ,k,λ) -difference set when k-λ≡6 or 10(mod 12);ii)when p ≡1(mod 3)is a prime number,then the equation p=x 2+y 2+xy has a nonnegative solution in integers x,y .
出处
《集美大学学报（自然科学版）》
CAS
北大核心
2000年第2期92-94,共3页
Journal of Jimei University：Natural Science
关键词
循环差集
必要条件
素数
不定方程
区组设计
Cyclic difference set
prime number
primitive root of unity
Hall polynomial
