Question 45
A company breeds monstrous creatures. If today the animal had $a$-scaly arms, $b$-scaly legs, and $c$-scaly head, then tomorrow it will have $b+c-a$, $c+a-b$, $a+b-c$ arms, legs, and head, and this evolution continues every day. Then prove that only those monstrous creatures born with an equal number of arms, legs, and heads at their first birth can live forever. Here it is $a, b, c \in \mathbb{N}$, and when any of the hands, feet, or head numbers are negative, the creature dies.