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)⌋


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

$I f 1, a^{2}, a^{3}, . . ., a^{n - 1} a r e t h e r o o t s$ $n t h o f u n i t y,$ $p r o v e t h a t : (1 + a) (1 + a^{2}) (1 + a^{3}) . . . (1 + a^{n - 1})$ $= n - 2 ⌊ \frac{n}{2} ⌋$
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