We consider the computation of eigenvectors x = (x1,..., xn) over the integers, where each component xi satisfies |xi | ≤ b for an integer b. We address various problems in this context, and analyze their computational complexity. We find that different problems are complete for the complexity classes NP, P NP � , FNP//OptP[O(log n)], FPNP, P NP, and NP NP. Applying the results, finding bounded solutions of a Diophantine equation v·x T = 0 is shown to be intractable
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