Question

Show that any positive odd.
- integer is of the form
6q +1 or 6q+3 or 6q +5
as here q is some integer​

Answer 1

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

then, by Euclid's division lemma

a = 6q + r ; where 0 < r < 6

so the values of r can be 1 ,3 and 5 as they are odd

when r = 1 ; a = 6q + 1

when r = 3 ; a = 6q + 3

when r = 5 ; a = 6q + 5

hence any odd positive integer can be of the form 6q + 1 , 6q+ 3 or 6q + 5