Question

Given a=2,c=1, and m=17, find the duration of the linear congruential generator when x₀ is 1 . Provide the generated sequence as well

Answer 1

A linear congruential generator is a type of pseudo-random number generator. The sequence is calculated using the equation xn+1= (a * xn + c) mod m. In this case, the generated sequence is 1, 3, 7, 15, 0, 1.

Step-by-step explanation:

A linear congruential generator is a type of pseudo-random number generator that produces a sequence of numbers based on a linear equation.

The equation is given by:
xn+1= (a * xn + c) mod m

where xn is the current value in the sequence, a, c, and m are constants.

In this case, we have a=2, c=1, and m=17. The initial value x0 is 1.

Let's calculate the sequence:

1. Step 1: Calculate x1 = (2 * 1 + 1) mod 17 = 3
2. Step 2: Calculate x2 = (2 * 3 + 1) mod 17 = 7
3. Step 3: Calculate x3 = (2 * 7 + 1) mod 17 = 15
4. Step 4: Calculate x4 = (2 * 15 + 1) mod 17 = 0
5. Step 5: Calculate x5 = (2 * 0 + 1) mod 17 = 1

The generated sequence is 1, 3, 7, 15, 0, 1.