Prove that n 1 , n 2 , n 3 , and n 4 are pairwise relatively prime if and only if gcd(n 1 n 2 , n 3 n 4 ) gcd (n 1 n 3 , n 2 n 4 ) 1 More generally, show that n 1 , n 2 , ,n k are pairwise relatively prime if and only if a set of lg k pairs of numbers derived from the n i are relatively prime ...

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Prove that n 1 , n 2 , n 3 , and n 4 are pairwise relatively

Question:

Prove that n₁, n₂, n₃, and n₄ are pairwise relatively prime if and only if gcd(n₁n₂, n₃n₄) = gcd (n₁n₃, n₂n₄) = 1. More generally, show that n₁, n₂, . . . ,n_k are pairwise relatively prime if and only if a set of ⌈lg k⌉ pairs of numbers derived from the n_i are relatively prime.