Linear congruential algorithm

If we take the linear congruential algorithm with an additive component of 0, Xn+1 = (aX_n) mod m

Then it can be shown that if m is prime and if a given value of produces the maximum period of m – 1 , then a^kwill also produce the maximum period, provided that is less than m and that and m - 1 are relatively prime. Demonstrate this by using X₀= 1and m = 31and producing the sequences for a^k= 3 3²3³and3⁴