# You are given any $51$ integers taken from $1, 2, \ldots, 100$. Prove that there are two that are relatively prime.

You are given any $51$ integers taken from $1, 2, \ldots, 100$. Prove that there are two that are relatively prime.

• Have you tried using standard techniques like the pigeonhole principal? – amarney Mar 27 '17 at 16:07
• Hello and welcome to math.stackexchange. Please tell us what you have tried, where you are stuck, whether you have solve a similar problem before. – Hans Engler Mar 27 '17 at 16:12
• @user5555: Such broad suggestions are never very helpful. Especially as the pigeonhole principle is not required here. – TonyK Mar 27 '17 at 16:13
• Presumably you need the additional constraint that the integers are all distinct. – Bungo Mar 27 '17 at 16:25
• @Bungo: That is implied by "You are given any $51$ integers." – TonyK Mar 27 '17 at 16:41

Hint: any two consecutive integers $n,n+1$ are relatively prime.