Computational indistinguishability: are function parameters known? I would like to clarify something about the definition of computational indistinguishability and pseudorandom number generators. Suppose we wanted to show that linear congruential generators of the form $x_t = ax_{t-1} + b \pmod m$ are not pesudorandom number generators. Then we wish to show that given a sequence of numbers $x_0, x_1, \ldots$, we can distinguish whether these numbers came from the lcg process above, or are coming from a uniform distribution (in polynomial time, with high probability, etc...). 

In doing so, do we assume that we are given the parameters $a,b$ and $m$? On the one hand, if we are given these parameters, then isn't this trivial? Just check if the given sequence satisfies the given lcg... On the other hand, even if we don't know $a,b,m$, there still clearly does exist a polynomial time algorithm that happens to have $a,b,m$ hard-coded into it that could be used to distinguish these sequences from truly random ones.

What is the correct interpretation here? Does it even make sense to ask whether LCGs are pseudorandom generators in the sense of computational indistinguishability?
You're right: If you know the setup, calculating the next output from any given $x$ is fully deterministic and you know everything already.

Even if you don't know $a$ and $b$, those are easy to calculate from three consecutive $x_i$. If $n$ is not known, its calculation is still pretty easy, given a few consecutive $x_i$.

Anyway, LCGs are very unsuitable for cryptographic tasks. That's why in pretty much every standard library you find a warning not to use the standard Random class for cryptographic protocols (at least for Java and Python I know those warnings are there).

Usually not the entire output is used, but only a part of it, because otherwise two consecutive numbers can't be equal (and ever change again afterwards). Such an RNG is good enough for almost all non-security-related context, where randomness is needed (it is good enough for a little randomness. But e.g. in simulations, where a lot of random numbers are needed, you want "better" randomness, e.g. from the Mersenne Twister). Anyway, predictable PRNGs (without the CS) based on any such construction is not suited for cryptography. For CSPRNGs, you can find a couple of designs on wikipedia.