View source for An integer and its successor are co-prime

The idea that '''an integer and its successor are co-prime''' is important in [[Number theory|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 co-prime to n.

The claim can easily be proven by stating that if two integers n and n + 1 were not co-prime, 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.

{{Claim
|Claim=An integer and its successor are co-prime
|Level=Proven
|Nature=Theoretical
|Counterclaim=
|DependentOn1=
|DependencyOf1=There are infinitely many primes
}}