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Power Expression, Prime? (Posted on 2015-01-22) Difficulty: 3 of 5
Can 19*8N + 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 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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