Section $2$ of AKS-Algorithm paper discusses the Idea of the Algorithm.
The paper uses the notation in equation $(2)$: $$(X+a)^n=X^n+a(\text{mod}\enspace X^r-1,n)$$
Does this notation mean $$[((X+a)^n-(X^n+a)\enspace\text{mod}\enspace n)\text{mod}\enspace X^r-1]$$
Also, how does it immediately follows that all primes satisfy the above equation? How can I prove "Mathematically" the two lines comments that succeed equation $(2)$ in the above paper?