29.

A, B, C,... . p , p 1 . , p 1. A , B b . . a,b,... . ( A, B . .) : A = 1 (mod </?(p)), 0 < <p 1; B be = 1 (mod </?(p)), 0 < <p 1 .. , -, p 1. , p 1, , , p 1.

A m (m < p 1) B. , m1 = ma (mod p) m1, B. B, m1,

b, m2 = m1 (mod p) m2, A. A m3 = (mod p)

m3 B. B, , m. , m4 = = maabe = m (mod p), . . ab = 1 (mod </?(p)), , aab = k</?(p) + 1 k mfc^(p)+1 = (mv(p))km = m (mod p), . . mv(p) = 1 (mod p) -.

. A B p = 23 (</?(23) = 22), A = 5, B b = 7. 5 = 1 (mod </?(23)) A = 9, B = 19. m = 17 A B A B m1 = 175 = 21 (mod 23), m1 = 21 B m2 = 217 = 10 (mod 23) A, m2 = 10 A B m3 = 109 = 20 (mod 23), , B

2019 = 17 (mod 23).

► 47

A B p = 167 15 21. 22 ( A B) 17 ( B A).