Question

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

Answer 1

Here is your answer in this picture
it's r = 0,1,2,3,4,5

Answer 2

by euclids division lemma
a= bq+ r
and b= 6 therefore r= 0,1,2,3,4,5
now,
6q ( even)
6q+1 ( odd)
6q+2 ( even)
6q+3( odd)
6q+4(even)
6q+5 (odd)
therefore, 6q+1, 6q+3 and 6q+5 are posotove odd integers.