Consider the polynomial f(x)=x2+x+1f(x) = x^2 + x + 1f(x)=x2+x+1. How many solutions exist for f(x)≡0(mod3k)f(x) \equiv 0 \pmod{3^k}f(x)≡0(mod3k) as k→∞k \to \inftyk→∞?
0
1
2
Depends on the parity of kkk