It is important that the induction hypothesis says n = 10*j + 7*k for some n >= 54 and

*nonnegative* integers j, k. Then j - 2 is not necessarily a nonnegative integer, so you have not proved that n is represented in a required way.

There are two options. One is to consider the cases j = 0 and j = 1 separately. This would still be a proof by regular induction. Another is to prove P(n) -> P(n + 7) where P is the induction hypothesis above. The induction step is obvious, but you need strong induction (though, strictly speaking, you use only P(n) and not P(k) for all 54 <= k < n + 7 in the proof of P(n + 7)). You also need to prove 7 bases cases.

See also

this tread.