ProjectEuler 435 Polynomials of Fibona - 拼圖
By Lily
at 2013-09-08T00:40
at 2013-09-08T00:40
Table of Contents
435. Polynomials of Fibonacci numbers
http://projecteuler.net/problem=435
費氏數列{f_n, n≧0}是由遞迴式f_n = f_(n-1) + f_(n-2)和首兩項f_0 = 0, f_1 = 1
所定義的數列。
令多項式F_n定義為F_n(x) = Σf_i x^i對0≦i≦n的和。
例如F_7(x) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8x^6 + 13x^7，代值x = 11可得
F_7(11) = 268357683。
令n = 10^15，請求出[ΣF_n(x)對0≦x≦100的和] mod 1307674368000 (= 15!)。
--
http://projecteuler.net/problem=435
費氏數列{f_n, n≧0}是由遞迴式f_n = f_(n-1) + f_(n-2)和首兩項f_0 = 0, f_1 = 1
所定義的數列。
令多項式F_n定義為F_n(x) = Σf_i x^i對0≦i≦n的和。
例如F_7(x) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8x^6 + 13x^7，代值x = 11可得
F_7(11) = 268357683。
令n = 10^15，請求出[ΣF_n(x)對0≦x≦100的和] mod 1307674368000 (= 15!)。
--
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By George
at 2013-09-09T23:26
at 2013-09-09T23:26
By Lily
at 2013-09-13T10:19
at 2013-09-13T10:19
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