Statements
(25) To divide an integer $b$ by a nonzero integer $d$, define a quotient $q$ and a remainder $r$ to be integers such that $b = q d + r$ and $| r | < | d |$. Such integers $q$ and $r$ always exist and are both unique for given $b$ and $d$. (26) To divide a polynomial $b ( x )$ by a nonzero polynomial $d ( x )$, define a quotient $q ( x )$ and a remainder $r ( x )$ to be polynomials such that $b = q d + r$ and $\deg ( r ) < \deg ( d )$. (Here $b ( x )$ and $d ( x )$ have real coefficients and the 0 polynomial is taken to have negative degree by convention.) Such polynomials $q ( x )$ and $r ( x )$ always exist and are both unique for given $b ( x )$ and $d ( x )$. (27) Suppose that in the preceding question $b ( x )$ and $d ( x )$ have rational coefficients. Then $q ( x )$ and $r ( x )$, if they exist, must also have rational coefficients. (28) The least positive number in the set $$\left\{ \left( a \times 2023 ^ { 2020 } \right) + \left( b \times 2020 ^ { 2023 } \right) \right\}$$ as $a$ and $b$ range over all integers is 3.