An integer and its successor are coprime
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The idea that an integer and its successor are coprime is important in number theory and plays a role in Euclid's proof that There are infinitely many primes. The claim is that any integer n + 1 will be coprime to n.
The claim can easily be proven by stating that if two integers n and n + 1 were not coprime, then the difference between the two would have to be a multiple of whatever prime(s) they share, but that difference would also be equal to 1. Thus there would have to be some number greater than 1 that is equal to 1, which is a contradiction.
Statement of the claim  An integer and its successor are coprime 
Level of certainty  Proven 
Nature  Theoretical 
Counterclaim  
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