How to prove that if $m = 10t+k $ and $67|t - 20k$ then 67|m? m, t, k are Natural numbers.
How can I prove that if $m = 10t+k $ and $67|t - 20k$ then 67|m ?

We have
$$10t+k=10t -200k+201k=10(t-20k)+(3)(67)k.$$
The result now follows from the fact that $67\mid(t-20k)$.
