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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 ?

  Submitted by Ravi Raja    
Rating: 2.6667 (9 votes)
Solution: (Hide)
2^(3) = 1 (mod 7). Hence 2^(3m) = 1 (mod 7), 2^(3m+1) = 2 (mod 7), and 2^(3m+2) = 4 (mod 7). Hence we never have 7 dividing 2^n + 1, and 7 divides 2^n - 1 iff 3 divides n.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2021-12-23 08:45:40
Some ThoughtsNo SubjectK Sengupta2008-02-07 05:14:03
re: la meme Janette mais autrement coifee!mark hartman2004-01-29 18:42:49
solutionmark hartman2004-01-29 18:34:50
Solutionla meme Janette mais autrement coifee!luminita2004-01-08 09:56:07
SolutionBrute forceDan Blume2004-01-02 16:44:11
SolutionSolutionRichard2004-01-02 10:51:26
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