Make and test a conjecture about the square of odd numbers.

The correct answer is: All odd square numbers have a remainder of 1 when divided by 8

Let the odd number be x
We know that standard form of odd number is (2n+1)
Squares of odd numbers are odd,
Since (2n + 1)² = 4n(n + 1) + 1,
and     n(n + 1) is always even.
All odd square numbers have a remainder of 1 when divided by 8.