Well, I have a system of congruences it is : $$n\equiv13\pmod{19}$$ $$n\equiv6\pmod{12}$$ I'm trying to prove that for any pair of integers $(u,v)$ the number $N=13\times12v+6\times19u$ is a solution to the system of equations above.
actually i don't know even how to begin :(.
Oh i forgot : $(u,v)$ satisfy $19u+12v=1$.