Question

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

Answer 1

Answer:

hope it helps.

thanks for giving me the opportunity to help you.

best of luck.

Answer 2

Answer:

let 'a' be any positive odd integer

Step-by-step explanation:

By Euclid division algorithm

a=b.q+r which b=4

where r= 0, 1,2,3 ; 0_< r<4

let r= 0

a=bq+r

a=4q+0

a=2(2q)

a=2m , where m= 2q

and

let r=2

a=bq+r

a=4q+2

a=2(2q+1)

a=2m, where m= 2q+1

hence, 4q, 4q+2 is divisible by 2

then, it is even number

therefore, any positive integer is of the form of 4q+1, 4q+3.

HOPE IT MAY HELP YOU