perplexus.info :: Just Math : Three Power Verification

Three Power Verification (Posted on 2016-01-20)

M is a positive integer such that 4^M + 2^M +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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