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The numbers 3^n -1 are never prime (if n 2>= 2), since they are always even.

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Question;The numbers 3^n -1 are never prime (if n 2>= 2), since they are always even. However,it sometimes happens that (3^n -1) /2 is prime. For example, (3^3 -1) /2 = 13 is prime.a) If n is even, show that (3^n - 1)/2 is always divisible by 4, so it can never be prime.b)Use a similar argument to show that if n is a multiple of 5 then (3^n - 1)/2 is never aprime.

 

Paper#60259 | Written in 18-Jul-2015

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