Question 44
(ROM 3) Suppose $p$ and $q$ are two different positive integers and $x$ is a real number. Form the product $(x+p)(x+q)$.
(a) Find the sum $S(x,n)=\sum(x+p)(x+q)$, where $p$ and $q$ take values from $1$ to $n$.
(b) Do there exist integer values of $x$ for which $S(x,n)=0$?
(a) Find the sum $S(x,n)=\sum(x+p)(x+q)$, where $p$ and $q$ take values from $1$ to $n$.
(b) Do there exist integer values of $x$ for which $S(x,n)=0$?