Question

Show that any positive odd integer is in the form (4m+1) or (4m+3) for same integer m

Answer 1

All positive integers can be represented in form 4m, 4m + 1, 4m + 2, 4m + 3.

Now, 2 can be taken out common from 4m and 4m + 2

( 2(2m) and 2(2m + 1))

So, these are even.

The rest are odd.

Thus 4m + 1 and 4m + 3 are odd.

Hence, proved.