Given the first n natural numbers, is it possible that every composite odd number is coprime with at least one even composite number and that no two odd numbers share the same even number. For example, given {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} we can see that (9,4), (15,8) are valid coprime pairs because each of 9 and 15 is paired with two different even composite numbers.
2026-03-28 04:34:26.1774672466
Coprimality in a given set of consecutive natural numbers
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A trivial solution pairs each odd composite number $k \le n$ with $k-1$. The OP's solution is a nontrivial solution for $n=20$.