Stupid Infinity

Algebra Level 4

If there be a polynomial \(f\left( x \right)\) which has distinct positive integer coefficients such that

\[f\left( 10 \right) =20\\ f\left( 8 \right) =16\]

Find how many polynomials satisfy the equation above.

  • If you believe your answer is infinity then enter 999 in the answer box.

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