Evaluate $\sqrt{2^{2014} + 2^{2011} + 2^{2006}} \pmod{17}$

96 Views Asked by At

Evaluate:

$$I = \sqrt{2^{2014} + 2^{2011} + 2^{2006}} \pmod{17}$$

$$I = \sqrt{2^{2006}\cdot (1 + 2^{5} + 2^{8} )} \pmod{17} = 2^{1003} \cdot \sqrt{2^8 + 2^5 + 1} \pmod{17}$$

The answer is $0$ somehow, how should I do this?