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

Show that any positive odd integer is of the form 6q+1,6q+3 ,6q+5 wher

1.	Show that any positive odd integer is of the form 6q+1,6q+3 ,6q+5 where q is some integer
Answer» According to Euclid\'s division lemma a=bq+r In this case b=5Possible remainders =0,1,2,3,4 and 51.When r=0a= bq+ra=6q+0a=6q (even)2.When r=1a=bq+ra=6q+1 (odd)3. When r=2a=bq+r a=6q+2 (even)4. When r=3 a=bq+r a=6q+3 (odd)5. When r=4 a=bq+r a=6q+4 (even)6. When r=5 a=bq+r a=6q+5 (odd)