+0  
 
0
396
4
avatar+468 

14^15 mod 15

 Jun 23, 2017
 #1
avatar+7076 
+1

14^1 mod 15 = 14

14^2 mod 15 = 1

14^3 mod 15 = 14

14^4 mod 15 = 1

.

.

.

We can see that 14^(2n+1) mod 15 = 14 and 14^(2n) mod 15 = 1

So that 14^15 mod 15 = 14. :D

 Jun 26, 2017
 #2
avatar+7076 
0

Now take an attempt on this problem:

\(14^{(1+2+3+4+5+6+...+107)}\pmod {15}=??\)

.
 Jun 26, 2017
 #3
avatar
+1

1+2+3+4+5+6...........+ 107 = [107 x 108] / 2 =5,778. So we have: 14^5,778 mod 15 =1

Guest Jun 26, 2017
 #4
avatar+20850 
+1

14^15 mod 15

 

\(\begin{array}{|rcll|} \hline \mathbf{ 14^{15} \pmod {15} =\ ? } \\\\ && 14^{15} \pmod {15} \quad &| \quad 14 \equiv -1 \pmod {15} \\ &\equiv& (-1)^{15} \pmod {15} \quad &| \quad (-1)^{15} = -1 \\ &\equiv& -1 \pmod {15} \\ &\equiv& -1 +15 \pmod {15} \\ &\equiv& 14 \pmod {15} \\\\ \mathbf{ 14^{15} \pmod {15} = 14 } \\ \hline \end{array} \)

 

 

laugh

 Jun 26, 2017
edited by heureka  Jun 26, 2017

11 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.