Question 89
We call a positive integer $N$ splendid, if
$$
N = (a - b)^2 + (b - c)^2 + (c - a)^2
$$
for some integers $a$, $b$ and $c$. If $M$ and $N$ are splendid positive integers, is the sum $M + N$ or the product $MN$ also necessarily splendid? How about the product $2MN$?
$$
N = (a - b)^2 + (b - c)^2 + (c - a)^2
$$
for some integers $a$, $b$ and $c$. If $M$ and $N$ are splendid positive integers, is the sum $M + N$ or the product $MN$ also necessarily splendid? How about the product $2MN$?