Question

Show that the square of any positive odd integer is of the form a 8m 1 for some integer m

Answer 1

since any odd positive integer m is of the form of 4q+1 or 4q+3.
if m =4q+1, then
m square =4q+1 whole square
=16q square +8q+1
=8q(q+1)+1
=8m+1. where m=q+1