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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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re: Solution | Comment 2 of 4 |
(In reply to Solution by broll)

The problem doesn't ask about M being a multiple of 3 but a power of 3.  

mod7 seems to show only that the expression can only be prime if M is a multiple of 3.
Considering mod3 you can also show M must be odd as well.

But I don't see how this rules out other multiples of 3 from potentially working.  15 does not (73 is the smallest prime factor) but I don't know about 21, 33, etc. or even 27 for that matter.

  Posted by Jer on 2016-01-21 07:49:36
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