Why 5 and 5+23=28 cannot both be primitive roots mod 23^2

Asked Dec 10 '19 at 05:12

Active Dec 10 '19 at 05:12

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I know how to show the first three parts, but I definitely have no idea about the fourth part. Thanks.

asked Dec 10 '19 at 05:12

JohnnyW

I am sorry for forgetting to put the first three parts. 1. show 5 is a primitive root mod 23. 2. find the number of primitive roots mod 23. 3. find all primitive roots mod 23, and I know how to do these parts. – JohnnyW Dec 10 '19 at 05:13
1

I presume because one of them solves $x^{22}\equiv1\pmod{23^2}$. – Angina Seng Dec 10 '19 at 05:18
solved it, thanks. – JohnnyW Dec 10 '19 at 13:28
https://math.stackexchange.com/questions/227199/order-of-numbers-modulo-p2 – lab bhattacharjee Dec 10 '19 at 14:39
@JohnnyWong: could post your solution as an answer? – J. W. Tanner Dec 10 '19 at 16:51

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