Determine the number of solutions x∈Z2kx \in \mathbb{Z}_{2^k}x∈Z2k to the congruence x2≡x(mod2k)x^2 \equiv x \pmod{2^k}x2≡x(mod2k) for k≥3k \geq 3k≥3.
222
444
2k2^k2k
kkk