# Is this polynomial familiar? - II

Algebra Level 2

$$f(x)$$ is a polynomial with integer coefficients. We have,

$$f(1)=1$$

$$f(2)=4$$

$$f(3)=9$$

$$f(4)=16$$

$$f(5)=25$$

$$f(6)=36$$

$$f(7)=49$$

$$f(8)=64$$

$$f(9)=81$$

$$f(10)=100$$

How many functions $$f(x)$$ satisfies the above conditions?

Details and assumptions:

• If your answer is infinity, enter $$0$$ as the answer.

More polynomials, anyone?

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