Question

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

Answer 1

Answer:

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

Answer 2

Answer:

Let 'a' be any positive integer

on dividing a by 4

q be quotient and r be remainder

By using Euclid's division lemma ,we have

a=4q+r where

$0 \leqslant r < 4$

i.e r= 1, 2, 3

a=4q

a=4q+1

a=4q+2

a=4q+3

but here 4q and 4q+2 are divisible by 2

whereas 4q+1 and 4q+3 are positive odd integer

i.e 'a'