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Art of Computer Programming, Volume 2, The: Seminumerical Algorithms by Donald E. Knuth

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Section 3.3.4

1. For generators of maximum period, the 1-D accuracy ν1 is always m, and μ1 = 2.

2. Let V be the matrix whose rows are V1, . . . , Vt. To minimize Y · Y, subject to the condition that Y ≠ (0, . . . , 0) and V Y is an integer column vector X, is equivalent to minimizing (V−1X) · (V−1X), subject to the condition that X is a nonzero integer column vector. The columns of V−1 are U1, . . . , Ut.

3. a2 ≡ 2a−1 and a3 ≡ 3a−2 (modulo m). By considering all short solutions of (15), we find that Image and Image, for the respective vectors (1, –2, 1) ...

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