show that any positive odd integers is of the form 6q+1,or 6q+3,or 6q+5 where q is some integer.

show that any positive odd integers is of the form 6q+1,or 6q+3,or 6q+

1.	show that any positive odd integers is of the form 6q+1,or 6q+3,or 6q+5 where q is some integer.
Answer» Any positive integer can be written in form a=bq+r, if we assume b=6 then r is greater than or equal to 0 and less than 6. Then a can be written in form a=6q+0, a=6q+1, a=6q+2, a=6q+3, a=6q+4, a=6q+5. Out of these a=6q, a=6q+2 and a=6q+4 can be written as multiple of 2, hence these forms represents even numbers.. Naturally other forms, which can not be written as multiple of 2 are representing odd numbers..