Interesting question

T. D. Noe noe at
Mon Aug 18 18:32:33 CEST 2008

>Jim Nastos wrote:
>> Interesting indeed.... isn't there some theorem that says that no
>> polynomial function can generate only primes? ... Or maybe that's a
>> single-variable polynomial.

For a single variable, suppose such a polynomial existed.
P(1) is prime; call it p.
So P(1)=0 (mod p).
So for any k, P(1 + kp) = 0 (mod p), which to be prime must be p itself.
So P(1 + kp) = P(1) for all k, which implies P is a constant function.

Neil Fernandez

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