摘要
给出了Erdos问题的几种等价表述,证明了如下结果:设{a_1(mod n_i)}_(i=1)~k(1<n_1<n_2<…<n_k)为不同模覆盖系,若不存在最小模超过n_1的不同模覆盖系,则必有模n_1为3n_1或4n_1的倍数;若诸模n_1全是无平方因子的奇数,则最小公倍数[n_1,…,n_k]至少有11个不同素因子。
Several equivalent versions of the Erds problem arc given and the following results arc also proved: Let {a_i(mod n_i)}_(i=1)~k (1<n_1<n_2…<n_k) be a covering system with distinct modulis. If there arc no covering systems whose mod uli are all distinct and greater than n_1, then for some i=1,…, k we have 3n_1|n_i or 4n_1|n_i. If all the moduli n_i are odd and squarefree, then their least common multiple [n_1,…, n_k] has at least 11 distinct prime factors.
