Question

Show that any odd positive integers is in the form of 4k+1 or 4k+3, k € z​

Answer 1

To show that

any odd positive integers is in the former of 4k+1 or 4k+3, k ∈z

Let a be any positive integer

From Euclid's Division lemma, a can be written as

$a=bk+r$

Where $0\le r<b$

If we take $b=4$

Then the possible values of r will be 0, 1, 2, 3

For $r=0$

$a=4k$ which is an even integer

For $r=1$

$a=4k+1$ which is an odd integer

For $r=2$

$a=4k+2$ which is an even integer

For $r=3$

$a=4k+3$ which is an odd integer

Therefore, odd positive integers are of the form $4k+1$ and $4k+3$

Hope this helps.

Know More:

Q: Show that square of any positive integer is of the form 4m or 4m+1 for some integer m.

Click Here: https://brainly.in/question/8545400

Q: Show that any positive even integer is of the form 8q, 8q + 2, 8q + 4, or 8q + 6, where q is some integer.

Click Here: https://brainly.in/question/331179

Q: Show that any positive integer is of the form 3q, 3q+1,3q+ 2 for some integer q.

Click Here: https://brainly.in/question/3038540