1. Primitive root help

for each m = 7^3 and m = 28

determine whether or not there exists a primitive root mod m, and if so find.

2. Originally Posted by Rakesh
for each m = 7^3 and m = 28
determine whether or not there exists a primitive root mod m, and if so find.
Not for $\displaystyle 28$, why not?

There is one for $\displaystyle 7^3$. Note $\displaystyle 2$ is primitive root for $\displaystyle 7$. But $\displaystyle 2^{7-1}\equiv 1(\bmod 7^2)$. So $\displaystyle 2+7=9$ is primitive root for $\displaystyle 7^3$ and $\displaystyle 9^{7-1}\not \equiv 1(\bmod 7^2)$.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}