On the Maximal Length of Two Sequences of Consecutive Integers with the Same Prime Divisors
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چکیده
The initial motivation of the present paper is the following problem of Erd6s and Woods, whose solution would be of interest in logic (see [3, 6, 11, 10, 16]): Does there exist an integer k >=2 with the following property : i f x and y are positive integers such that for l<=i<=k, the two numbers x+ i and y+i have the same prime factors, then x=y. For each integer n->2, let us denote by Supp (n) the set of prime factors of n. The only known examples of positive integers (x,y, k )wi th l<=x=2 and
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تاریخ انتشار 1989