Question

What is the remainder when x^2013 + 1 is divided by (x^2-1)?

Answer 1

$({x}^{2013} + 1) = { {x}^{2} }^{1006} {x}^{1} + 1 \\ by \: substituting \: {x}^{2} = 1 \\ { {x}^{2} }^{1006} x + 1 = {1}^{1006} x + 1 \\ = x + 1 \\ hence \: remainde \: = x + 1$