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How Many ? (Posted on 2004-01-02) Difficulty: 3 of 5
How many positive integers 'n' are there such that [(2)^n + 1] is divisible by 7 ?

See The Solution Submitted by Ravi Raja    
Rating: 2.6667 (9 votes)

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solution | Comment 4 of 6 |
This problem is easily solved with mod 7 arithmetic (ie Base 7 arithmetic - usually learned in number theory).
We are looking for solutions for n such that 2^n = 6 mod 7.
2^1 = 2 mod 7
2^2 = 4 mod 7
2^3 = 1 mod 7
2^4 = 2*(2^3) mod 7 = 2 mod 7
2^5 = 2*(2^4) mod 7 = 4 mod 7
2^6 = 2*(2^5) mod 7 = 1 mod 7
etc.
There is no solution for n.
  Posted by mark hartman on 2004-01-29 18:34:50
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