Find the smallest field $F$, which has characteristic $2$, where the polynomial $x^{14}+1$ decomposes into linear factors.
I've tried to decompose it (to be honest, to guess the decomposition) in some fields (2, 4, 8) - but I've no idea how to find roots. Should I guess only 1 root $x_0$ - and after divide $x^{14}+1$ by $x-x_0$ modulo $2$? And continiue until i find all roots?