Prove a random generated number is uniform distributed

Given a random number generator to generate a number between [0,N), how to prove this number is uniform distributed.
Any suggestion?
Checkout the Chi Square Test for Uniformity.

It's a measure of how uniform your results are.

The idea is, you generate N numbers from you PRNG. You break them into intervals and check how closely the intervals have the same number of entries.

If you want something more formal: http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf
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