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How many integers \(n\) can be used such that the quantity \(|2n^2+23n+11| \) results in a prime number?

 Nov 29, 2020
 #1
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+1

How many integers "n" can be used such that the quantity abs[2n^2+23n+11]  results in a prime number?

 

n =0,  -10,  -12 gives the following prime numbers =11,  19,  23

 Nov 29, 2020
 #2
avatar+112086 
+1

\(|2n^2+23n+11|=|(n+11)(2n+1)|\)

 

If this is to be prime then one of the factors must be +/-1 and the other must be  +/- a prime number.

 

so either

\(n+11=\pm1\qquad and \qquad |2n+1|\;\;is \;\;prime\\ or\\ 2n+1=\pm1 \qquad and \qquad |n+11|\;\;is \;\;prime\\\)

 

solve and you will have your answer,

 Nov 29, 2020

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