The following problem is to be proven with induction:
You want to buy some cats, but cats are only sold in batches of 3 or 5. Prove inductively that for any n ≥ 8, there is a way to purchase exactly n cats.
I got as far as $3x+5y=n\implies 3k+5q=n+1$.
Also I proved the base case for $n=8$ which is $x=1,y=1$
However, I don't understand how to prove the inductive step.