How do I prove that two consecutive integers are relatively prime? In other words, how do I show if two integers have no common factors other than 1? Thanks

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- December 1st 2008, 12:15 PMTitaniumXrelatively prime
How do I prove that two consecutive integers are relatively prime? In other words, how do I show if two integers have no common factors other than 1? Thanks

- December 1st 2008, 12:22 PMMoo
- December 1st 2008, 12:28 PMvincisonfire
Suppose you have some integer whose factorization is

. The consecutive integer is

. Let be a prime dividing . Then doesn't divide otherwise it would divide the difference . This is impossible.

Therefore, there is no prime integer that divide both and . In other words they have no common factors or are relatively prime.