Consider the periodic discrete-time exponential time signal x[n] = e^m(2π/N)n

Show that the fundamental period of this signal is N0 = N/ gcd(m, N), where gcd(m, N) is the greatest common divisor of m and N—that is, the largest integer that divides both m and N an integral number of times. For example, gcd(2, 3) = 1, gcd(2, 4) = 2, gcd(8, 12) = 4. Note that N0 = N if m and N have no factors in common