Question 179
Let $S$ be the set of all integers of the form $x^2 + 3xy + 8y^2$ where $x$ and $y$ are integers.
a. Show that if $u$ and $v$ are in $S$, then so is $uv$.
b. Can an integer of the form $23k + 7$, with $k$ an integer, belong to $S$?
a. Show that if $u$ and $v$ are in $S$, then so is $uv$.
b. Can an integer of the form $23k + 7$, with $k$ an integer, belong to $S$?