I have met the following theorem from the book Introduction to Algorithms (3rd ed.) in the number theory section. The theorem states that
Prove that if $a>b>0$ and $c=a+b$, then $c \bmod a=b$.
Please help. In my mind, the main aspect is that because $a>b>0$, it means $c$ is also more then $0$ and each $a$ and $b$, and also $c/a=1$, so remainder is equal automatically to $b$, or $c=1 \cdot a+b$ (because a>b). Please tell me if I am correct.