The formula appears to be expressed in a couple of ways, each one using a different variable. The one that Google provides, for instance, is
, where
is the order number for the maximum.
On the other hand, the formula used in HSC Physics appears to be expressed as
, where
refers to the order of the maximum, therefore indicating the same thing as the
expressed within Google's formula. It also follows that
must be an integer, which is consistent with your initial suggestion.
Additionally, consider the following question, which highlights that
must be an integer:
A monochromatic light is passed through two slits separated by 0.0100 mm. It is observed that the 3rd order maximum on the viewing screen is formed at an angle 11.0° relative to the midpoint of the two slits.
What is the wavelength (in nm) of the monochromatic light?
In the case of this question,
(i.e. an integer).
I hope this helps!