If-1-a-2-a-3-a-n-1-are-the-roots-nth-of-unity-prove-that-1-a-1-a-2-1-a-3-1-a-n-1-n-2-n-2-

Question Number 113336 by 175mohamed last updated on 12/Sep/20

I f 1, a^{2}, a^{3}, \dots, a^{n - 1} a r e t h e r o o t s

n t h o f u n i t y,

p r o v e t h a t : (1 + a) (1 + a^{2}) (1 + a^{3}) \dots (1 + a^{n - 1})

= n - 2 ⌊ \frac{n}{2} ⌋