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,