Answer :

Let a be an positive odd integer, and let b = 4


By, using Euclid's division lemma,


a = 4q + r, where r is an integer such that, 0 ≤ r < 4


So, only four cases are possible


a = 4q or


a = 4q + 1 or


a = 4q + 2 or


a = 4q + 3


But 4q and 4q + 2 are divisible by 2, therefore these cases are not possible, as a is an odd integer.


Therefore,


a = 4q + 1 or a = 4q + 3.


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