Here is a simple strategy for designing an infinite pseudo-random number generator: **Linear Congruential Generator (LCG)** A linear congruential generator is a widely used pseudo-random number generator that can produce an infinite sequence. Here is a basic strategy: 1. Choose a large prime number `m` (for example, `m = 2^31 - 1 = 2147483647`). 2. Choose an integer `a` (for example, `a = 1664525`) such that `a` is relatively prime to `m` (that is, `a` and `m` have no common factors other than 1). 3. Choose an integer `c` (for example, `c = 1013904223`) that is odd and between `0` and `m-1` (inclusive). 4. Initialize a seed value `x0` (for example, `x0 = 123456789`), which is an arbitrary integer between `0` and `m-1` (inclusive). **Algorithm for generating infinite sequences: 1. When starting to generate the sequence, set `x = x0`. 2. Generate the next value of the sequence `x_next`, calculated using the following formula: `x_next = (a * x + c) mod m` where `mod` is the modulus operator (i.e., remainder operator). 3. Generate the current value of the sequence as output: `output = x`. 4. Update the seed value for the next iteration: `x = x_next`. 5. Return to step 2. **Sample Python Code:** ```python def generate_infinite_sequence(): m = 2**31 - 1 # large prime a = 1664525 # integer coprime with m c = 1013904223 # odd integer between 0 and m-1 x0 = 123456789 # initial seed value x = x0 while True: x_next = (a * x + c) % m yield xx = x_next # Example Usage: sequence = generate_infinite_sequence() for _ in range(10): # print the first 10 values print(next(sequence)) ``` This strategy generates an infinite sequence where each value is between `0` and `m-1` (inclusive). The LCG algorithm is widely used in many applications, including simulation, modeling, and cryptography. NOTE: Although this sequence is infinite, it is not truly random because it is generated via a deterministic formula. However, the properties of the LCG algorithm make the sequences appear sufficiently random and uniform in practice.