信息安全数学基础 普通高等教育“十一五”国家级规划教材 教学课件 ppt 作者 裴定一 徐祥习题答案 信息安全数学答案.pdf

1 1.1 1111111101, 3FD 1.2 2 1.3 374133280 1.4 510 × 11766 − 737 × 8142 = 6. 1.5 a = pt1a , b = pt2 b , (p, a ) = (p, b ) = 1, ord (a) = t ,ord (b) = t .  t 1 1 1 1 p 1 p 2 1 ≥ t , a + b = pt2 (pt1−t2 a + b ) ord (a + b) ≥ t =min{ord (a),ord (b)}, 2 1 1 p 2 p p t t , pt1−t2 a + b = 0, (p, pt1−t2 a + b ) = 1, 1 2 1 1 1 1 1.6 1, 2, , n pi n , 1, 2, , n pi i p pi+1 n − n , i i+1 p p λ ordp (n!) = i( n − n ) i i+1 p p i=1 λ = n i p i=1 1.7 2|n(n + 1)(2n + 1) n = 3s + r, 0 ≤ r 3, n + 1 = 3s + (r + 1), 2n + 1 = 3(2s + r) − (r − 1), r − 1, r, r + 1 3 3|n(n + 1)(2n + 1) 6|n(n + 1)(2n + 1) 1.8 (a, b)m |am, (a, b)m |bm, (a, b)m 0 x, y ∈ Z ax + by = (a, b) amx + bmy = (a, b)m. c c|am, c|bm, c|(a, b)m (