Question 88
A positive integer is a palindrome if and only if it reads the same from left to right as from right to left; for example $1221$ and $74847$ are palindromes. An $n$-digit positive integer $k$ is written in decimal as $\overline{a_{n-1}a_{n-2}\cdots a_0}$. Prove that if $k$ is a palindrome, then $k^2$ is a palindrome if and only if $a_0^2 + a_1^2 + \cdots + a_{n-1}^2 \lt 10$.