多元的覆盖同余式

Covering Systems of Congruences with Many Dimensions

将覆盖同余式推广到多元覆盖的情形 ,证出了当 p1 ,p2 ,… ,pr为奇素数时 ,覆盖系 ai ∏rj=1pαijjki=1 各模两两不同的充要条件为〈ui1 ,… ,uir〉(〈φ( pα1i1 ) ,… ,φ( pαrir )〉) ki=1为一个 r元的覆盖系 ,又对一个多元的覆盖系〈ui1 ,… ,uin〉( mod〈mi1 ,… ,min〉) ki=1令 dj| [m1 j,m2 j,… ,msj]则有 k≥ s≥ t( d1 ,… ,dn)

The covering systems of congruences have been studied by many authors.The purpose of this paper is to study the systems of congruences with many dimensions.If {〈u i1 ,u i2 ,…,u in 〉(〈m i1 ,m i2 ,…,m in 〉)} k i=1 is a k th CS, then k≥s≥t(d 1,d 2,…,d n).