Question

show that any positive odd integer is of the form 4q+ 1or 4q+3 where q is some integer

Answer 1

here  is ur answer....
lets take the value of q=1
put it in the given equation that is  4q+1=4+1=5
so, this is an odd positive integer
hence an odd positive integer is always in the form 4q+1
hope it helps uh..........

Answer 2

Step-by-step explanation:

Let a be the positive integer.

And, b = 4 .

Then by Euclid's division lemma,

We can write a = 4q + r ,for some integer q and 0 ≤ r < 4 .

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

Taking r = 0 .

a = 4q .

Taking r = 1 .

a = 4q + 1 .

Taking r = 2

a = 4q + 2 .

Taking r = 3 .

a = 4q + 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 .

Hence , it is solved .