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  
 
0
108
1
avatar

\(If $a,b,c$ are positive integers less than $13$ such that \begin{align*} 2ab+bc+ca&\equiv 0\pmod{13}\\ ab+2bc+ca&\equiv 6abc\pmod{13}\\ ab+bc+2ca&\equiv 8abc\pmod {13} \end{align*}then determine the remainder when $a+b+c$ is divided by $13$.\)

Please help I really am bad at these sorts of things.

Thanks!

 Jan 5, 2019

Best Answer 

 #1
avatar
+1

Check here and see how many solutions there are:

 

https://www.wolframalpha.com/input/?i=2ab+%2B+bc+%2B+ca+%3D0,+%5Bab+%2B+2bc+%2B+ca%5D+mod+13+%3D6abc,+%5Bab+%2B+bc+%2B+2ca%5D+mod+13+%3D8abc,+solve+for+a,+b,+c

 Jan 5, 2019
 #1
avatar
+1
Best Answer

Check here and see how many solutions there are:

 

https://www.wolframalpha.com/input/?i=2ab+%2B+bc+%2B+ca+%3D0,+%5Bab+%2B+2bc+%2B+ca%5D+mod+13+%3D6abc,+%5Bab+%2B+bc+%2B+2ca%5D+mod+13+%3D8abc,+solve+for+a,+b,+c

Guest Jan 5, 2019

13 Online Users

avatar