# A little long recursion

Algebra Level 4

If $$a$$, $$b$$ and $$c$$ are complex numbers that satisfy: $a^2+b^2+c^2=-3$ $a^3+b^3+c^3=-46$ $a^4+b^4+c^4=-123$ And it's known that the value of $$a+b+c$$ is an integer.

Find $$(a^{10}+b^{10}+c^{10}) \mod 1000$$.

×