Question

Use division algorithms to show that any positive odd integer Is of the forme 6q +1 or 6q+3 or6q+5

Answer 1

r=1
6q+r
6q+1 is positive integer

r=3

6q+3 is positive interger and even integer

r=5

6q+5 is positive integers


hence 6q+1,6q+3,6q+5 are positive integers