Question
If x^4+x^3+x^2+x+1 = 0, then the value of x^{25} is
If x^4+x^3+x^2+x+1 = 0, then the value of x^{25} is
Given
Multiply both sides with x to raise the power of leading term to 5
Subtracting (1) from (2) gives
Then
Using power rule for exponent
x^{25} = (x^5)^5 = 1^5 = 1
Therefore
the value of x^{25} is 1