0 votes 0 votes $x^{2}+x+1$ is a factor of $\left ( x+1 \right )^{n}-x^{n}-1$ whenever $n$ is odd $n$ is odd and multiple of $3$ $n$ is an even multiple of $3$ $n$ is odd and not a multiple of $3$ Set Theory & Algebra factors isi2004 engineering-mathematics + – Tesla! asked Apr 3, 2017 • edited Nov 8, 2019 by go_editor Tesla! 547 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Keep $n=3$ it would come out to be $3x^2 +3x ,$ so it would be a factor of $x^2 +x+1$ Kaluti answered Apr 4, 2017 • edited May 12, 2019 by Lakshman Bhaiya Kaluti comment Share Follow See all 4 Comments See all 4 4 Comments reply Kaluti commented Apr 4, 2017 reply Follow Share Therefore answer should be c 0 votes 0 votes Akriti sood commented Apr 4, 2017 reply Follow Share @kaluti,how 3*(x^(2)) +3*(x) is a multiple of x^(2) +(x)+1?would'nt 1 be a remainder then?? 0 votes 0 votes ankitgupta.1729 commented Mar 16, 2019 reply Follow Share Answer will be (D) https://math.stackexchange.com/questions/3150295/x2x1-is-a-factor-of-x1n-xn-1-whenever?noredirect=1&lq=1 https://math.stackexchange.com/questions/1237256/find-n-such-that-x2-x-1-is-a-factor-of-x1n-xn-1 2 votes 2 votes ds733124 commented Jul 9, 2021 reply Follow Share If w is a cube root of unity, then w is a root of1+x+x^2=0. Now x+1=-x^2 Then if n is odd and not multiple of three, (-x^2)^n+-x^n-1=-(x^n)^2-x^n-1=0 So correct answer is D 0 votes 0 votes Please log in or register to add a comment.
