1. arithmetic in Z/nZ

Any help greatly appreciated!!

I can do similar ones such as x^6 - 14 = 0 in Z/65Z, but this one with 4 to the power of x, has me stuck.

Solve the following equation:

4^x +2 = 0 in Z/29Z,

2. Originally Posted by rmangan

Solve the following equation: $4^x +2 \equiv 0 \mod 29$.
the equation has no solution: first note that: $4^x=(2^x)^2.$ now we have $\frac{29 - 1}{2}=14$ and $\frac{29^2 - 1}{8}=105.$ therefore: $\left(\frac{-2}{29} \right)=(-1)^{14}(-1)^{105}=-1. \ \Box$