- #1
kingwinner
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Claim: n! + 1 and (n+1)! + 1 are relatively prime.
How can we prove this? Can we use mathematical induction?
Base case: (n=1)
gcd(2,3)=1
Therefore, the statement is true for n=1.
Assuming the statement is true for n=k: gcd(k! + 1,(k+1)! + 1)=1 (induction hypothesis), we need to show that it's true for n=k+1. But I am stuck here. How can we use the induction hypothesis to prove this?
Or am I even on the right track thinking of using induction?
Thanks for any help!
How can we prove this? Can we use mathematical induction?
Base case: (n=1)
gcd(2,3)=1
Therefore, the statement is true for n=1.
Assuming the statement is true for n=k: gcd(k! + 1,(k+1)! + 1)=1 (induction hypothesis), we need to show that it's true for n=k+1. But I am stuck here. How can we use the induction hypothesis to prove this?
Or am I even on the right track thinking of using induction?
Thanks for any help!