If I have a congruence equation, says $x^{15} - x^{10} + 4x - 3 \equiv 0 \pmod{7}$
Then can I use Fermat's little theorem like this: $(x^{6})^2 \cdot x^3 - x^6 \cdot x^4 + 4x - 3 \equiv 0 \pmod{7}$ $ x^3 - x^4 + 4x - 3 \equiv 0 \pmod{7}$
Update
Should it be $x^{14}x - x^7x^3 - 4x - 3 \equiv 0 \pmod{7}$ $x^2x - x.x^3 - 4x - 3 \equiv 0 \pmod{7}$ $x^3 - x^4 - 4x - 3 \equiv 0 \pmod{7}$ ? Thanks,