The question is inspired by a simple game called FizzBuzz. The idea is to select multiples of 3 or 5 from a closed sequence of positive integers <1, 2, .. 100>.
It turns out that congruence relation $k^4 \equiv 1\ (mod_{15})$ contains whatever that is not the multiple of 3 or 5. What's the intuition behind this - what's so magical about taking the fourth power modulo 15?
The group $(\mathbb{Z}/15\mathbb{Z})^{\times}$ is such that:
All of in this group have 1 as their 4th power. So that should explain the chart.