Question

use division algorithm to show that any positive odd integer is of the form 6q+q,or 6q+5,where q is some integer​

Answer 1

Answer:

Let a be any positive integer and b=6.

Then by division algorithm,

a=6q+r where r=0,1,2,3

So, a is of the form 6q,

6q+1,6q+2,6q+3

Therefore if a is an odd integer then a is of the form 6q+q or 6q+5 or q.

Hence, any positive odd integer is of the form 6q+q or 6q+5 or q.