Prove the following by induction: Every natural number n > 6 can be written as n = 3j + 4k for some integers j and k

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I have tried solving this question but haven't been able to. Pls if anyone could provide any other views so I could crack it it would be greatly appreciated

This was my attempt at solving the question: For n = 7, we can write 7 as 3(1) + 4(1) since both j and k are integers (j = 1, k = 1).

Inductive Step: Assume that for some arbitrary positive integer m > 6, we can write m = 3j + 4k for some integers j and k.

Now, I want to show that this implies the statement for m + 1.

Starting with the assumed statement for m: m=3j+4k

Adding 1 to both sides: m+1=3j+4k+1

Now, we can express m+1 as 3(j+1)+4(k−1).

Since j and k are integers, (j+1) and (k−1) are also integers.