Practice - Happy Number

A happy number is defined as: start with any positive integer, replace it with the sum of the squares of its digits, and repeat until the number equals $1$ or loops endlessly in a cycle that doesn't include $1$.

For example, $19$ is happy: $1^2 + 9^2 = 82$, $8^2 + 2^2 = 68$, $6^2 + 8^2 = 100$, $1^2 + 0^2 + 0^2 = 1$.

Write a function that determines if $n$ is happy. Use digit extraction (modulo and division) and cycle detection.