Abstract
Consider a sequence of ℓ positive integers a 1, a 2,…, a ℓ with a j − a j−1 = k(>0), j=2,3,…,ℓ. An element b of A is called a relative prime number if b is a relatively prime to any element a of A with a≠ b. In this paper, we show that for every k, there is a positive integer ℓ 0( k) such that for all integers ℓ⩾ℓ 0( k), there exists a sequence A with length ℓ which has no relative prime number.
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