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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