Question

using Euclid division lemma show that any positive odd integer is of the form 4q+1 or 4q+3 where qis some integer



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Answer 1

Answer:

Thus, we can say that any odd integer can be written in the form 4q + 1 or 4q + 3 where q is some integer

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

AnswEr:

Let us Consider that a & b are two positive integers.

Now, By Using Euclid's Division Lemma

Then, a = bq + r

Here, [ 0 < r = < b]

• b = 4

So, r can be 0, 1, 2 & 3

If r = 0

= a = 4q + 0

= a = 4q

This is an even integer.

If r = 1

= a = 4q + 1

This is an odd Integer.

If r = 2

= a = 4q + 2

This is an even integer.

If r = 3

= a = 4q + 3

This is an odd Integer.

$\rule{150}2$

So, any odd integers is in the form of 4q + 1 & 4q + 3.

Hence, Proved!