Interview Question
I think the question is missing something, because I can't come up with any computationally feasible solution(Turing decidable), mathematical feasible ones... yeah... because it's quite easy to see that the amount of possible integer coefficient polynomials are countable, and the amount of values it can take are uncountable.
Let f be the polynomial.
f(1) and f(f(1)+1)
The solution was discussed in one of the 'gifts' here
It's discussed in Lipton's blog post, some mathematical gifts.
Wow, no links allowed in the comments... careercup is such an amazing website...
Evaluate on 0 and x, where x has the following property...
For every positive integer k, x^k can not be expressed as a integral linear combination of {x^i | i\in N-{k}}...
In fact, any transcendental number will do because transcendental number are algebraically independent to itself.
It seems to be imposible or you missed something
- akormushin November 27, 2010