- #1
MathematicalPhysicist
Gold Member
- 4,699
- 371
the question is as follows:
gcd(n,10)=1, i need to prove that there exists a k>=1 such that 10^k-1 is divisible by n.
now i thought to look at the set of the remainders of division by 10, i got from what is given that this set is {1,3,9,7} cause n and 10 don't have other common factors besides one. now i thought to look first at n=7, and I am not sure there exists an appropiate k such that 10^k-1 is divisble by 7.
i think that this question the way it's satated isn't valid am i correct or wrong here?
gcd(n,10)=1, i need to prove that there exists a k>=1 such that 10^k-1 is divisible by n.
now i thought to look at the set of the remainders of division by 10, i got from what is given that this set is {1,3,9,7} cause n and 10 don't have other common factors besides one. now i thought to look first at n=7, and I am not sure there exists an appropiate k such that 10^k-1 is divisble by 7.
i think that this question the way it's satated isn't valid am i correct or wrong here?