Algebra: Let p(X) = X7-X ∈ Z7[X]

Let p(X) = X⁷-X ∈ Z₇[X]. Show that p(a) = 0, for all a ∈ Z₇.
This video proves that the polynomial P(x) = x⁷ – x is identically null in the ring of integers modulo 7 (Z₇).

Solution (video):