On sequences containing at most 3 pairwise coprime integers
On sequences containing at most 3 pairwise coprime integers
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DOI：
10.1090/s0002-9947-1973-0327710-7
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发表时间：
1973-09
影响因子：
1.3
通讯作者：
S. Choi
中科院分区：
文献类型：
--
作者：
S. Choi
鄂尔多斯猜想，不能选择k+1个两两互素整数的最大自然数不超过n，其中k>；1和n>；pk表示第k个素数，等于不超过n的自然数的个数，它们至少是前k个素数之一的倍数。我们知道，当k=1和2时，猜想成立。本文证明了k=3时猜想的真实性。
It has been conjectured by Erdos that the largest number of natural numibers not exceeding n from which one cannot select k+ 1 pairwise coprime integers, where k > 1 and n > Pk, with Pk denoting the kth prime, is equal to the number of natural numbers not exceeding n which are multiples of at least one of the first k primes. It is known that the conjecture holds for k = 1 and 2. In this paper we establish the truth of the conjecture for k = 3.