Question

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

Answer 1

Let "a" be any positive integer and 'b'=4
then r can be 0,1,2,3
by euclid's algorithm,
a=bq+r
therefore
a=4q
a=4q+1
a=4q+2
a=4q+3
here 4q and 4q+2 are even positive integer
odd integer is of the form 4q+1 and 4q+3
PLEASE MARK AS BRAINLIEST!!!!!!!

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 .