Show that any positive odd integer is of the form 4m+1 or 4m+3, where m is some integer

Step-by-step explanation:

I am taking q as some integer.

Let a be the positive integer.

And, b = 4 .

Then by Euclid's division lemma,

We can write ,for some integer

°•° Then, possible values of r is 0, 1, 2, 3 .

But a is an odd positive integer, so a can't be 4q , or 4q + 2

[ As these are even ] .

•°• a can be of the form 4q + 1 or 4q + 3 for some integer q .