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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 Solution | Comment 1 of 7
2^n is congruent only to 2, 4, or 1 mod 7, so 2^n+1 is congruent only to 3, 5, or 2 mod 7. Hence there are 0 positive integers n such that 2^n + 1 (or 2^(n+1) for that matter) is divisible by 7.
  Posted by Richard on 2004-01-02 10:51:26
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