# Non-zero coefficients

Probability Level 5

Consider the polynomial

$f(x) = (x^{20} + x^{13} + 1)^{33}.$

When fully expanded, how many terms have a non-zero coefficient?

Details and assumptions

As an explicit example, since $(x^2 + 1)^3 = x^6 + 3x^4 + 3x^2 + 1$, there are 4 terms with a non-zero coefficient.

You may use the fact that ${ 33 \choose 2 } = 528, {34 \choose 2 } = 561$ and ${ 35 \choose 2 } = 595$.

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