Question

show that any postive odd integer is in form of 4q+ 1 or 4q+3

Answer 1

Here is your answer...

This answer is done by using Euclids division algorithm.

Hope this helps you.

Answer 2

According to Euclid division lemma
a=bq+r. where 0<r<B

let a=4q+r. o<r<4. where r=0,1,2,3

if r=0
a=4q+0
a=4q
2(2q)
=2q. where q=2q€integer
even number

if r=1
a=4q+1
2(2q)+1
where q=2q
4q+1 is an odd number
if r=3
2×2q+2+1
2(2q+1)+1
where q=2q+1


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