Question

hello guys....









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

Step-by-step explanation:

Let 'a' be any positive odd 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

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

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

i.e 'a'