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# Trouble Proving Cyclotomic Polynomial Identity

We are required to show that
$$x^n-1=\prod_{d|n}\phi_{d}(x)$$
I am aware this is considered a trivial identity and that there are numerous ways to prove it, however, I am having trouble understanding this specific argument used by the author.
I am particularily confused as to how he was motivated in defining various variables such as d = n/g where g = hcf(n,k) etc.

http://people.maths.ox.ac.uk/earl/complex/0164.pdf – Author’s proof