the operation mod, how it works with polynomial...

[esoli]

hi, anyone can explain to me how the operation mod works with this expansion? I know just b mod a=c if b=a*n+c!

the definition of right cyclic shift,
v⁽¹⁾(x) = v_n−1 + v₀x + · · · + v_n−2xⁿ⁻¹
= v_n−1 + v₀x + · · · + v_n−2xⁿ⁻¹ + v_n−1xⁿ − v_n−1xⁿ
= xv(x) − v_n−1(xⁿ − 1)
= xv(x) mod (xⁿ − 1)