The question is , if f(n)= 1+10+10^2 + + 10^n , where n is

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sigh1342

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the question is , if f(n)= 1+10+10^2 +... + 10^n , where n is integer.
find the least n s.t. f(n) is divisible by 17 , I have no idea about it.
 

Answers and Replies

  • #2


What is the remainder if you divide...
1 by 17?
10 by 17?
100 by 17?
...
a+b by 17, if you know it for a and b?

That should help.
 
  • #3


sigh1342 said:
the question is , if f(n)= 1+10+10^2 +... + 10^n , where n is integer.
find the least n s.t. f(n) is divisible by 17 , I have no idea about it.

It should also help to recognize that 9 times the sum plus 1 is a power of 10. Thus Fermats Little theorem re primes P dividing A^(P-1) - 1 may apply.
 
  • #4


You can also find n by "brute force", i.e. check if f(1), f(2), f(3), ... is divisible by 17. Use http://www.wolframalpha.com/ or write a small program in your programming language of choice.
 
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