Minimum number of terms resulting from the product of two polynomials with a given number of terms Given two integers ($n$, $m$), what is the smallest number of terms that could result from the product of two polynomials with $n$ and $m$ non-zero terms respectively?
That is, what is the smallest number of non-zero terms that could result from the following product:
$$(a_1 x^{b_1} + \dots + a_n x ^ {b_n})(c_1 x^{d_1} + \dots + c_m x ^ {d_m})$$
where $a_i$ and $c_i$ are non-zero.
The answers to this question show that the answer cannot be $1$ in all cases, but it is obviously less than $n+m$, which should theoretically be the maximum.

Consider $(x - 1)(x^n+ \dotsb + 1) = x^{n+1} -1$
