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Three Power Verification (
Posted on 20160120
)
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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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 20160120 22:28:29
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