We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
-1
37
1
avatar+54 

Find the order of 15 mod 257.

 May 9, 2019
 #1
avatar+22180 
+2

Find the order of 15 mod 257.

 

1. 257 is a prime and
2. \(257-1 = 2^8\) is a power of a prime, so
3. the order of 257 must also be a power of two. The order is \(2^k\) for some \(k= 0,1,2,\ldots, 8\)

 

Test:

\(\begin{array}{|r|r|l|} \hline k & 2^k \\ \hline 0 & 1 & 15^1 \equiv 15 \pmod{257} \\ 1 & 2 & 15^2 \equiv 225 \pmod{257} \\ 2 & 4 & 15^4 \equiv 253 \pmod{257} \\ 3 & 8 & 15^8 \equiv 16 \pmod{257} \\ 4 & 16 & 15^{16} \equiv 256 \pmod{257} \\ 5 & \color{red}32& 15^{32} \equiv {\color{red}1} \pmod{257} \\ \hline \end{array}\)

 

The order of 15 mod 257 is 32

 

source see: https://math.stackexchange.com/questions/2271153/calculate-the-order-of-3-modulo-257

 

laugh

 May 10, 2019

6 Online Users