Question

Show that any positive odd integer is of the form 4q + 1 or 4q +3, where q is some positive integer 23

Answer 1

Is there any mistake in your qstn?..I think the right qstn is this one.. and if you have meant this qstn which I have uploaded.. then the answer is this.. and if.. its no then i dont know the answer

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 .