Question

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

Answer 1

Let, any positive odd integer be"a" ,b=6
a=bq + r ;0<r<b

a= 6q+r ; 0 <r<6

r=0,1,2,3,4,5

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

here,
6q+0 , 6q+2 , 6q+4 are even integer
And
6q+1 , 6q+3 and 6q+5 are odd integer