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Power Expression, Prime? (Posted on 2015-01-22)

Can 19*8^N + 17 be a prime number for a nonnegative integer N?

If so, give an example.
If not, prove it.

No Solution Yet Submitted by K Sengupta

Rating: 3.0000 (1 votes)

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Solution (spoiler)

Comment 1 of 1

No, it can never be prime

If N is even, then it is divisible by 3 (prove by considering the equation mod 3)

If N = 2m + 1, then it is divisible by 13 (prove by considering the equation mod 13). The use of 13 was indicated directly by noting that 19*8 + 17 = 169, whose only prime factor is 13.

If N = 2m + 3, then it is divisible by 5 (prove by considering the equation mod 5).

Posted by Steve Herman on 2015-01-22 16:46:32

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