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anonymous
 5 years ago
Theory of Numbers: If n is element of Z, prove that (4^n  1) is divisible by 3.
anonymous
 5 years ago
Theory of Numbers: If n is element of Z, prove that (4^n  1) is divisible by 3.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This took me awhile. I used mathematical induction. So we prove it works for 1: 4^11=3 which is divisible by 3. Then we assume it works for 4^n1 and check if it then works for 4^(n+1)1 So 4^(n+1)1=4(4^n1)+3 Since we assume 4^n1 is divisible by 3, lets write it as 3a So 4(3a)+3. 3(4a+1). This is a factor of 3 and therefore divisible by 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well we assume it works or n and check if it then works for (n+1)
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