Random Number Generation

For a ValueLabs coding assessment, implement a deterministic pseudorandom number generator without using Python's random module. Use a linear congruential generator to produce a sequence of integers within an inclusive range.

The generator must update its state using:

state = (1664525 * state + 1013904223) % 2^32

Map each updated state into the requested range using the remainder operator.

Formal Specification

Implement generate_random_numbers(seed, count, lower, upper), where:

1. seed is the initial non-negative integer state.
2. count is the number of values to generate.
3. lower and upper define an inclusive output range.
4. Return a list containing exactly count integers.
5. Each returned value must satisfy lower <= value <= upper.
6. The same inputs must always produce the same output.

For each value, first update the state, then calculate lower + state % (upper - lower + 1).