In numeral system with base $c$ the sum of two non-zero numbers $aba_(c)$ and $bab_(c)$ equals $xyxy_(c)$. Find all values of $a$ and $b$.

Question

As the title says I have to find all possible values of $a$ and $b$ when given the base $c$. I don't really know how to approach this problem. I found out that it's true when $a+b=c+1$. Would appreciate any kind of help.