Prove that x^4+x^3+x^2+x+1∣x^(4n)+x^(3n)+x^(2n)+x^n+1

kadejoset 2022-07-18 Answered
Prove that x 4 + x 3 + x 2 + x + 1 x 4 n + x 3 n + x 2 n + x n + 1
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Answers (1)

Eve Good
Answered 2022-07-19 Author has 18 answers
X 4 + X 3 + X 2 + X + 1 = X 5 1 X 1
X 4 n + X 3 n + X 2 n + X n + 1 = X 5 n 1 X n 1
Now, use the fact that X 5 1 | X 5 n 1 and that for n not divisible by 5 we have
g c d ( X 5 1 , X n 1 ) = X g c d ( 5 , n ) 1 = X 1
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