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Three Power Verification (Posted on 2016-01-20) Difficulty: 3 of 5
M is a positive integer such that 4M + 2M +1 is a prime number.

Can there be any instance where M is not a power of 3?

Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
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Solution | Comment 1 of 4
It suffices to consider the expression mod7. The cycle is {0,0,3}; so unless m=0,1, or a multiple of 3, m is divisible by 7, and so cannot be prime.
  Posted by broll on 2016-01-20 22:28:29
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