\begin{eqnarray*}a^{4n+1}-a &=& a(a^{4n}-1)\\ &=& a(a^4-1)(\mathrm{neki\ izraz})\\ &=& a(a-1)(a+1)(a^2+1)(\mathrm{neki\ izraz})\\ &=& a(a-1)(a+1)(a^2-4+5)(\mathrm{neki\ izraz})\\ &=& [(a-2)(a-1)a(a+1)(a+2)+5(a-1)a(a+1)](\mathrm{neki\ izraz})\end{eqnarray*}