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＝x2＋y2＋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＝x2＋y2＋xy has a nonnegative solution in integers x，y．
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