Question 1173733
.


                                        For your info:



I found  (thanks to  GOOGLE)  that post in wwww.algebra.com 

to which you missed to refer,  relevant to this problem.


https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1160694.html


I read that solution and came to the conclusion that it is  INCORRECT,  unfortunately.



            That solution would work for polynomials with the constant term different from  1,


            but  DOES  NOT  work for polynomials with the constant term equal to  1.



            From the other side,  only such polynomials with the constant term  1  are of interest --- 
            --- all the others are  OUT  OF  the  INTEREST,  because for them the statement is  TRIVIAL.



I also looked with this request to popular  "people"  web-sites,  and noticed,  that they repeat the same error.



/\/\/\/\/\/\/\/



After some time break, I browsed in the Internet again, looking for appropriate sources.



I found this article online


http://www.cs.umd.edu/~gasarch/BLOGPAPERS/polyprimes.pdf


where the statement is proved 


<pre>
    Let f(x) ∈ Z[x]. There are an infinite number of y ∈ Z such that f(y) is not prime.
</pre>

See Colollary 2.2 in this article.