Question

Show that any positive add integer is of the form 6q+1,6q+3 or 6q+5 where q is some integer

Answer 1

Step-by-step explanation:

Let a be any positive odd integer and b = 6,so there exist q.

a = bq + r [ r = 0 or 1 or 2 or 3 or 4 or 5 ]

So, 1) a = 6q + 0

a = 6q

2) a = 6q+ 1

3) a = 6q + 2

4) a = 6q + 3

5) a = 6q + 4

6) a = 6q + 5

So, Any positive odd integer is of form 6q+1,6q+3 or 6q+5. [Because 1),2) and 3) are even]