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Old 2015-10-14, 14:19   #33
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

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Quote:
Originally Posted by davar55 View Post
Regarding your example, expanding the polynomial x^2 + x + 41.

Is there any way to PROOVE this is prime for
all integers x between 0 and 39 inclusive,
without actually testing or enumerating the range?
Good question, it was an olympiad problem in 1987, see: http://www.artofproblemsolving.com/w...lems/Problem_6
So if we know that the above f(x)=x^2+x+41 is prime for f(0),f(1),f(2),f(3) then we know that it is also prime for f(4),..,f(39).
As I can remember there is a proof that there is only a finitely many such n value for that we can apply the statement, and we know all of them.
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