Given any positive integers k3 and λ,let c（k,λ）denote the smallest integer such that u ∈ B（k,λ）for every integer uc（k,λ）that satisfies the congruences λv（v-1）≡0（mod k（k-1））and λ（u-1）≡0（mod k-1...Given any positive integers k3 and λ,let c（k,λ）denote the smallest integer such that u ∈ B（k,λ）for every integer uc（k,λ）that satisfies the congruences λv（v-1）≡0（mod k（k-1））and λ（u-1）≡0（mod k-1）.In this article we make an improvement on the bound of c（k,λ）provided by Chang in[4]and prove that c（k,λ）exp{k<sup>3k<sup>6</sup></sup>}.In particular,c（k,1）exp{k<sup>k<sup>2</sup></sup>}.展开更多
Given any setK of positive integers and positive integer λ, letc(K,λ) denote the smallest integer such that v ∈B(K, λ) for every integerv≥c(K, λ) that satisfies the congruencesλv(v-1) ≡ 0 (modβ(K)) and λ (v-...Given any setK of positive integers and positive integer λ, letc(K,λ) denote the smallest integer such that v ∈B(K, λ) for every integerv≥c(K, λ) that satisfies the congruencesλv(v-1) ≡ 0 (modβ(K)) and λ (v-1)=≡ (modα(K)). LetK 0 be an equivalent set ofK, k andk* be the smallest and the largest integers inK 0. We prove that c(K, λ) ≤exp expQ 0 where $$Q_0 = \max \left\{ {2^{(2p(K_0 )^2 - k + k^2 \log _4 k)p(K_0 )^4 } ,(k^{k^2 } 4^{2y - k - 2} )^{(\begin{array}{*{20}c} y \\ 2 \\ \end{array} )} } \right\},$$ $p(K_0 ) = \prod\nolimits_{l \in K_0 } l $ andy=k*+k(k?1)+1.展开更多
Let k be any integer and k≥3. In this article it is proved that the necessary condition υ=k (mod k(k-1)) for the existence of an RB(v,k,1) is sufficient whenever u>exp{exp{k12k2}}.
基金Supported by NSFC Grant No.19701002 and Huo Yingdong Foundation
文摘Given any positive integers k3 and λ,let c（k,λ）denote the smallest integer such that u ∈ B（k,λ）for every integer uc（k,λ）that satisfies the congruences λv（v-1）≡0（mod k（k-1））and λ（u-1）≡0（mod k-1）.In this article we make an improvement on the bound of c（k,λ）provided by Chang in[4]and prove that c（k,λ）exp{k<sup>3k<sup>6</sup></sup>}.In particular,c（k,1）exp{k<sup>k<sup>2</sup></sup>}.
基金This work was supported by the National Natural Science Foundation of China (Grant No.19701002)and Hou Yingdong Foundation.It was also partially supported by Climbing Foundation of Northern Jiaotong University.
文摘Given any setK of positive integers and positive integer λ, letc(K,λ) denote the smallest integer such that v ∈B(K, λ) for every integerv≥c(K, λ) that satisfies the congruencesλv(v-1) ≡ 0 (modβ(K)) and λ (v-1)=≡ (modα(K)). LetK 0 be an equivalent set ofK, k andk* be the smallest and the largest integers inK 0. We prove that c(K, λ) ≤exp expQ 0 where $$Q_0 = \max \left\{ {2^{(2p(K_0 )^2 - k + k^2 \log _4 k)p(K_0 )^4 } ,(k^{k^2 } 4^{2y - k - 2} )^{(\begin{array}{*{20}c} y \\ 2 \\ \end{array} )} } \right\},$$ $p(K_0 ) = \prod\nolimits_{l \in K_0 } l $ andy=k*+k(k?1)+1.
基金the National Natural Science Foundation of China (No.19701002) HuoYingdong Foundation.
文摘Let k be any integer and k≥3. In this article it is proved that the necessary condition υ=k (mod k(k-1)) for the existence of an RB(v,k,1) is sufficient whenever u>exp{exp{k12k2}}.
