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Perfect Prime Provision? (Posted on 2013-10-27) Difficulty: 3 of 5
Each of 2N + 1 and 3N + 1 is a perfect square for a positive integer N.

Can 5N + 3 be a prime number?
If not, prove it.
If so, provide an example.

No Solution Yet Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

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Solution Answer Comment 2 of 2 |
Let A^2=2N+1 and B^2=3N+1. Then, 5N+3=(8N+4)-(3N+1)=4(2N+1)-(3N+1)=4A^2-B^2=(2A+B)(2A-B). Therefore, 5N+3 is not prime.

  Posted by Math Man on 2013-10-29 21:16:07
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