Question

prove that any odd number square can be written in the form of 8x+1.
(don't show examples)

Answer 1

We know any odd number can be written as (2n+1).

So, (2n+1)²=4n²+4n+1=4n(n+1)+1

Now, note that either one of n or n+1 has to be even as they are consecutive. So, square of a odd number is of form 8k+1.