Question 41
Consider a set of integers $M$, having the properties:
i) $1$ belongs to $M$;
ii) if $x$ and $y$ are in $M$, then $2x + 3y$ is in $M$;
iii) if $x, y$ are integers such that $4x - 3y$ belongs to $M$, then $x \cdot y$ belongs to $M$.
Prove that $M$ contains the numbers $2$, $3$, $4$, $5$ and $2019$.
i) $1$ belongs to $M$;
ii) if $x$ and $y$ are in $M$, then $2x + 3y$ is in $M$;
iii) if $x, y$ are integers such that $4x - 3y$ belongs to $M$, then $x \cdot y$ belongs to $M$.
Prove that $M$ contains the numbers $2$, $3$, $4$, $5$ and $2019$.