Numbers Equal to Sum of Squares of Digits/Historical Note

Historical Note on Numbers Equal to Sum of Squares of Digits

This result was presented without proof in François Le Lionnais and Jean Brette: Les Nombres Remarquables of $1983$.

However, they failed to note that it is important to stress the fact that it depends on the number base.

While it holds for base $10$, it is not true for base $3$:

$5$ expressed in base $3$ is $12$, while $1^2 + 2^2 = 5$