I just need confirmation that I've done my math right.
If $a(x) = x^4 + x^3 + x + 1$ and $b(x) = x^2 + x + 1$ are binary polynomials, find binary polynomials s(x) and r(x) such that
$x^4 + x^3 + x + 1 = s(x)(x^2 + x + 1) + r(x)$, where $r(x)$ is of degree at most $1$.
$s(x)$ can be $x$ or $x + 1$
if $s(x) = x$, then $r(x)$ would be $x^3$
if $s(x) = x + 1$, then $r(x)$ would be $x + 1$
Which one is correct? Would they both be correct?