Question

prove that any oposite odd integer is of form 6x + 1, 6x+1, 6x+3, or 6x+5.

Answer 1

Step-by-step explanation:

To show any positive odd Integers is of the form 6q+1 ,6q+3 and 6q+5

let 'a' be any positive odd integer and b=6

By using Euclid's division lemma;

a=bq+r

a=6q+r

since, positive integers are

( r=0 ). a=bq+0

a=6q

( r=1 ) a=6q+1

( r=2) a=6q+2

( r=3) a=6q+3

( r=4) a=6q+4

( r=5) a=6q+5

Since 6q+1,6q+3,6q+5 aren't divisible by 2

i.e; Any positive odd Integers are in the form of 6q+1,6q+3,6q+5.