+44 If a,b,c are positive integers less than 13 such that \(\begin{align*} 2ab+bc+ca&\equiv 0\pmod{13}\\ ab+2bc+ca&\equiv 3abc\pmod{13}\\ ab+bc+2ca&\equiv 8abc\pmod {13} \end{align*}\) then determine the remainder when a+b+c is divided by 13.
+52 Question answered by heureka and Alan here : https://web2.0calc.com/questions/help-me_17340
