31.

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W1, W2,... , Wn . . i- (1 = i ^ n) pi1 pi2, ri = pi1 pi2 </?(), 0 < < </?(), (, </?(ri)) = 1 , , = 1 (mod </?()). :

W: 1 ,1

W1 m W2, :

1) m > min(r1 ,r2), m , 1 2 ;

2) 1 < 2 , m 1 (m1 = mai (mod r1)), 2 (m2 = (mod r2)), r1 > r2, m 2 (m1 = ma2 (mod r2)), 1 (m2 = m^1 (mod r1));

3) m2 W2.

W2 m2 , , m2 , W1. 1 < 2 , m2 2, 1, 1 > 2 , m2 1, 2. 1 < 2 : m^2 = a2 = m1 (mod r2) m^1 = maiai = m (mod r1) -.

. W1 p11 = 7,p12 = 13, 1 = pnp12 = 91,^(91) = 72, 1 = 5,1 = 29, W2 p21 = 11,p22 = 23, r2 = 253,^(253) = 220, 2 = 31, 2 = 71. W1 W2 , W2 m = 41 W1. . . 2 > 1 , 1 , 2: m1 = 41 5 = 6 (mod 91), m2 = 671 = 94 (mod 253). m2 W1. m2 = 94, W1, , W2, 2, 1: 9431 (mod 253) = 6, 629 (mod 91) = 41.

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