If a, b, c are positive integers less than 13 such that

2ab + bc + ca = 0 (mod 13)

ab + 2bc + ca = 2abc (mod 13)

ab + bc + 2ca = 3abc (mod 13)

then determine the remainder when a + b + c is divided by 13.

See the solution here: https://web2.0calc.com/questions/modular-number-theory#r6