Question

Let a, b, c are distinct integers and w, w² are the imaginary cube roots of unity. If minimum value of |a +bw +cw²| +| a +bw² + cw| is n^1/4 where n ∈ N, then find the value of n.

Answer 1

Minimum value will occur when 

a – b = K, a – c = –K

i.e. K = 1

a – b = 1a – c = –1 

with a & b being least possible value integer