[math-fun] The minimal polynomial for e^(i π/170) has a "balanced ternary" coefficient list.

In[87]:= CoefficientList[MinimalPolynomial[E^(I π/170), x], x] Out[87]= {1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1} (Presumably unexceptional.) In[88]:= FromDigits[%, x] (1 - x^2 + x^4 - x^6 + x^8 + x^34 - x^36 + x^38 - x^40 + x^42) // Expand Out[88]= 1 + x^170 —rwg