"How to find the order of 20 mod 20801"

Asked Nov 10 '24 at 09:43

Active Nov 17 '24 at 02:14

Viewed 55 times

I did try the order test which gave me an answer $60$, but the actual answer is $15$.

I also tried the Chinese remainder theorem but by letting $x=20^n$ and got an answer $1$, which was obvious but I do not really know how to solve this, since $20$ is not a prime applying order test also becomes a problem

edited Nov 17 '24 at 02:14

Guruprasad

asked Nov 10 '24 at 09:43

user263066

2

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Nov 10 '24 at 09:44
1

A shorter title would be: "How to find the order of $20\mod 20801$". – Jean Marie Nov 10 '24 at 10:33
$20$ has order $5,15,5$ mod $11,31,61$ so has order ${\rm lcm}(5,15,5)=15,$ mod $,{\rm lcm}(11,31,61) = 20801,,$ cf. Remark here. $\ \ $ – Bill Dubuque Nov 10 '24 at 18:16

"How to find the order of 20 mod 20801"

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