MathDB

Let

a_1,a_2,a_3,\dots

be infinite sequence of positive integers satisfying the following conditon: for each prime number

p

, there are only finite number of positive integers

i

such that

p|a_i

. Prove that that sequence contains a sub-sequence

a_{i_1},a_{i_2},a_{i_3},\dots

, with

1 \le i_1<i_2<i_3<\dots

, such that for each

m \ne n

, \gcd(a_{i_m},a_{i_n})\equal{}1.

Problem Statement