Question

What is the reason behind taking b =6 in the Question: Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. [3 MARKS]

Answer 1

Let a be a given integer.

On dividing a by 6 , we get q as the quotient and r as the remainder such that

a = 6q + r, r = 0,1,2,3,4,5

when r=0

a = 6q,even no

when r=1

a = 6q + 1, odd no

when r=2

a = 6q + 2, even no

when r = 3

a=6q + 3,odd no

when r=4

a=6q + 4,even no

when r=5,

a= 6q + 5 , odd no

...Any positive odd integer is of the form 6q+1,6q+3 or 6q+5