privatestaticreadonlylong[]f100=newlong[125];privatestaticreadonlylong[]m100=newlong[125];// init in main functionm100[0]=1;m100[1]=1;f100[0]=1;f100[1]=1;privatestaticboolPeriod200(longn){for(intp=2;p<125;p++){f100[p]=(f100[p-1]+f100[p-2])%n;m100[p]=f100[p];}for(inti...
Pisano PeriodPisano Period FnmodPFnmodP的循环节mm是使得Fm≡0(modP)∧Fm+1≡1(modP)Fm≡0(modP)∧Fm+1≡1(modP)的最小正整数mm。 易知m∣k⇔Fk≡0(modP),Fk+1≡1(modP)m∣k⇔Fk≡0(modP),Fk+1≡1(modP)。 Part.1Part.1 我们需要先证明一些引理。 引理11 设p∈P,n∈N+p∈P,...
Pisano PeriodPisano Period FnmodPFnmodP的循环节mm是使得Fm≡0(modP)∧Fm+1≡1(modP)Fm≡0(modP)∧Fm+1≡1(modP)的最小正整数mm。 易知m∣k⇔Fk≡0(modP),Fk+1≡1(modP)m∣k⇔Fk≡0(modP),Fk+1≡1(modP)。 Part.1Part.1 我们需要先证明一些引理。 引理11 设p∈P,n∈N+p∈P,...
假如,αi=1,对于f(pi),我们这么求: 考虑模数p为奇素数的情况:假如5是模p的二次剩余,我们对Fibp,Fibp+1做二项式展开:Fibp+1=22p+15((p+11)5+(p+13)53+…+(p+1p)5p)≡12(1+5p−1)≡1(modp)Fibp=22p5((p1)5+(p3)53+…+(pp)5p)≡5p−1≡1(modp)所以此时有皮萨诺周期f(p)∣p−...
\(\text{Pisano Period}\) \(F_n\bmod P\)的循环节\(m\)是使得\(F_m\equiv0\pmod P\wedge F_{m+1}\equiv1\pmod P\)的最小正整数\(m\)。 易知\(m\mid k\Leftrightarrow F_k\equiv0\pmod P,F_{k+1}\equiv1\pmod P\)。
In number theory, the nth Pisano period, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph...
简介 With this fantastic app you can calculate Pisano Periods and Fibonacci Series. Also you can share the series through Twitter, Facebook and your email. - Pisano Periods - F(mod m) - Fibonacci Series - Fibonacci number - Fn - Share ...
(though I'm pretty sure no one has asked about it on English Competitive Programming Forums), but this seems to be a direct application of the Pisano Period. However, I am only able to find anO(m^2)algorithm, which does not suffice the condition of this problem. Even though there ...
(though I'm pretty sure no one has asked about it on English Competitive Programming Forums), but this seems to be a direct application of the Pisano Period. However, I am only able to find anO(m^2)algorithm, which does not suffice the condition of this problem. Even though there ...
The Pisano period factorization method has been proved slightly better than the recently developed algorithms such as quadratic sieve method and the elliptic curve method. This paper ideates new insights in the area of integer factorization problems....