<sod>A non-example is <math>3</math> in the ring of integers modulo <math>26</math>; while <math>3^3 \equiv 1 \pmod{26}</math> and thus <math>3</math> is a cube root of unity, <math>1 + 3 + 3^2 \equiv 13 \pmod{26}</math> meaning that it is not a ''principal'' cube root of unity.<eod>
<sod>A non-example is <math>3</math> in the ring of integers modulo <math>26</math>; while <math>3^3 \equiv 1 \pmod{26}</math> and thus <math>3</math> is a cube root of unity, <math>1 + 3 + 3^2 \equiv 13 \pmod{26}</math> meaning that it is not a ''principal'' [[cube root of unity]].<eod>