Find the flaw with the following proof that every postage of

Find the flaw with the following proof that every postage of 3 cents or more can be formed using just 3-cent and 4-cent stamps.

{Basis step:} We can form postage of 3 cents with a single 3-cent stamp and we can form postage of 4 cents using a single 4-cent stamp.

Solution

There can be four types of postage stamp requirement with value as

4k , 4k + 1 , 4k + 2 and 4k + 3

4k and 4k + 3 can be formed directly from the 4 cent and 3 cent stamps

4k + 2 = 4( k - 1 ) + 6 , which can be formed using 4 cent and 3 cent stamps

4k + 1 = 4( k - 2 ) + 9 , which can be formed using 4 cent and 3 cent stamps

but if k = 1 in above , the rule fails