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Divisibility (Posted on 2007-01-08) Difficulty: 3 of 5
Let A be an integer, P an odd prime and n=3 be the smallest integer for which A^n - 1 is divisible by P.
Determine the smallest integer m for which (A+1)^m - 1 is divisible by P.

No Solution Yet Submitted by atheron    
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re(2): Some more thoughts | Comment 4 of 6 |

As I see it, the problem with using A=4 and p=3 is that the problem states that "n=3 be the smallest integer for which A^n - 1 is divisible by p." Clearly 4^n - 1 is divisible by 3 for n=2 and n=1 so this example violates the conditions of the problem. I do agree however, that p divides zero, but atheron appears to be ruling out this case for otherwise n=0 would be the smallest integer for which A^n - 1 is divisible by p. 


  Posted by Dennis on 2007-01-09 12:44:23
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