Question 53
Consider the solutions of the system
$$
\left\{\begin{array}{l}
2019=a+b-c \\
2019=a^{2}+b^{2}-c^{2}
\end{array}\right.
$$
where $a$, $b$ and $c$ are integers.
a) Find at least one solution of the system.
b) Verify that the number of solutions is finite.
$$
\left\{\begin{array}{l}
2019=a+b-c \\
2019=a^{2}+b^{2}-c^{2}
\end{array}\right.
$$
where $a$, $b$ and $c$ are integers.
a) Find at least one solution of the system.
b) Verify that the number of solutions is finite.