Factorise 53 using the difference of two squares method.
What do you notice about this approach in factorising 53?
We first notice that 53 is prime, but we proceed anyway.
$\lceil \sqrt{53} \rceil = 8$, and $8^2 - 53 = 11$, which is not a perfect square.
Trying many integers incrementing upwards from 8 leads to $27^2 - 53 = 26^2$.
That is,
$$ 53 = (27+26)(27-26) = 53 \times 1$$
The difference of two squares method leads to a factorisation where one of the factors is 1.
Note the author's solution states that 53 is a prime that cannot be expressed as the difference of two squares, but we have just shown that it can.