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What is the multiplicative order of a product of two integers $\mod n$?
Standard texts prove that $\textrm{ord}_n(ab)=\textrm{ord}_n(a)\,\textrm{ord}_n(b)$ when $\textrm{gcd}(\textrm{ord}_n(a),\textrm{ord}_n(b))=1$. What if they are not relatively prime? Here $\textrm{...
- 11.8k
0
votes
1
answer
73
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Prime power decomposition
$x^{147} \equiv (((x^{7})^{7})^{3})\equiv x^{3}(mod7)$
How does $x^{147}$ simplify into $x^{3}(mod7)$
What Corollary is responsible for this?
Edit:
Fermat's Little Theorem is needed:
147 = 3 * 7 *...
- 289
0
votes
1
answer
495
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Generator of $Z_p^*$ with large p
I have to find a generator for $Z_{p}^*$. The prime number p is $2425967623052370772757633156976982469681$. My prime factors for (p-1) is according to 1 $f_k=(5,457,571,62429281,174394544633,...
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