Question

2. Show that every positive odd integer is of the form 49 +1 or 4q+3, where is
some integer.
Solutions​

Answer 1

Step-by-step explanation:

Let a be any positive odd integer and b=4

So by applying division lemma to a,b

a=4q+r where o≤r<4

When r=0

a=4q+0=4q=2(2q)

When r=1

a=4q+1=4q+1

When r=2

a=4q+2=4q+2=2(2q+1)

When r=3

a=4q+3=4q+3

Since 4q,4q+2 are multiple of 2 so they are even numbers

So every positive odd integer is of the form (4q+1) or (4q+3) where q is some integer