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 –...

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

Then it can be shown that if m is prime and if a given value of produces the maximum period ofm– 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 X
₀= 1andm= 31and producing the sequences fora^k
= 3 3²3³and3⁴