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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
+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
+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

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