[imath]\text{ord}_p[/imath]

[logistic_guy]

Compute the following \(\displaystyle \text{ord}_p\) values:

(a) \(\displaystyle \text{ord}_2(2816)\).
(b) \(\displaystyle \text{ord}_7(2222574487)\).
(c) \(\displaystyle \text{ord}_p(46375)\) for each of \(\displaystyle p = 3, 5, 7, \text{and} \ 11\).

 

[khansaheb]

Compute the following \(\displaystyle \text{ord}_p\) values:

(a) \(\displaystyle \text{ord}_2(2816)\).
(b) \(\displaystyle \text{ord}_7(2222574487)\).
(c) \(\displaystyle \text{ord}_p(46375)\) for each of \(\displaystyle p = 3, 5, 7, \text{and} \ 11\).

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[logistic_guy]

\(\displaystyle \bold{(a)}\)

\(\displaystyle 2816 = 2^8 \times 11\)

Then,

\(\displaystyle \text{ord}_2(2816) = 8\)

 

[logistic_guy]

\(\displaystyle \bold{(b)}\)

\(\displaystyle 2222574487 = 7^5 \times 132241\)

Then,

\(\displaystyle \text{ord}_7(2222574487) = 5\)

 

[logistic_guy]

\(\displaystyle \bold{(c)}\)

Le us start with \(\displaystyle p = 3\)

\(\displaystyle 46375 = 5^3 \times 7 \times 53\)

Then,

\(\displaystyle \text{ord}_3(46375) = 0\)

 

[logistic_guy]

\(\displaystyle \bold{(c)}\)

When \(\displaystyle p = 5\)

\(\displaystyle 46375 = 5^3 \times 7 \times 53\)

Then,

\(\displaystyle \text{ord}_5(46375) = 3\)

 

[logistic_guy]

\(\displaystyle \bold{(c)}\)

When \(\displaystyle p = 7\)

\(\displaystyle 46375 = 5^3 \times 7 \times 53\)

Then,

\(\displaystyle \text{ord}_7(46375) = 1\)