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Consider m=24, i.e., Xn+1 =(aXn) mod 24. (Hint: This is a common case for a linear...

Consider m=24, i.e., Xn+1 =(aXn) mod 24. (Hint: This is a common case for a linear congruential algorithm when m is a power of 2.)

What should be the value of a to achieve the maximum period?

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Answer #1

so and so on

In general

The maximum period possible is

Which is

So we need to find an whose period modulo is as large as possible

We can check that

As we must have we can say that any of the values will work

And that the maximum period we will get is 2

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