Question

show that square of odd positive integer is in the form of 8q+1 for integer q

Answer 1

Here is the answer to your question.

Any odd positive integer is of the form 4q + 1 or 4q + 3 for some integer q.
I'm using here 8m+1
At the place of 8q+1
When n = 4q + 1,
Hence, square of any positive odd integer is of the form 8m + 1, for some integer m.