# Odd Coprimes

Let a be an odd integer. Prove that and are relatively prime for all distinct positive integers n and m.

- 12 August, 2012 -
- Article, Math Problems -
- Tags : 104 problems, number theory, titu
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Because are distinct, then we can impose an arbitrary ordering on them such that . Suppose that for any prime , we find that by definition

Because only when . However, since is odd, cannot be , therefore, . Because every prime factor of cannot divide , then by definition, these two expressions are relatively prime for any distinct .