Question

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

Answer 1

let a be any positive integer and b is 6 .then by euclid algorithm a =bq+r and 0 < r<b .
so the possible remainders are 0 ,1,2,3,4,5
therefore 6q,6q+1 ,6q+2,6q+3,6q+4,6q+5
but a can be a positive odd integer
so a is 6q +1,6q+3,6q+5