Conocemos el número de Fibonacci , F n = F n-1 + F n-2.
Los primeros números de Fibonacci son 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …. .
Aquí hay algunos datos interesantes sobre el número de Fibonacci:
1. Patrón en los últimos dígitos de los números de Fibonacci: Los
últimos dígitos de los primeros números de Fibonacci son:
0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, ...
La serie de últimos dígitos se repite con una longitud de ciclo de 60 (consulte esto para obtener explicaciones de este resultado).
C++
// C++ program to demonstrate that sequence of last
// digits of Fibonacci numbers repeats after 60.
#include <bits/stdc++.h>
using namespace std;
#define max 100
int main()
{
long long int arr[max];
arr[0] = 0;
arr[1] = 1;
int i = 0;
// storing Fibonacci numbers
for (i = 2; i < max; i++) {
arr[i] = arr[i - 1] + arr[i - 2];
}
// Traversing through store numbers
for (i = 1; i < max - 1; i++) {
// Since first two number are 0 and 1
// so, if any two consecutive number encounter 0 and
// 1 at their unit place, then it clearly means that
// number is repeating/ since we just have to find
// the sum of previous two number
cout << i << endl;
if ((arr[i] % 10 == 0) && (arr[i + 1] % 10 == 1)) {
break;
}
}
cout << "Sequence is repeating after index " << i
<< endl;
}
C
// C program to demonstrate that sequence of last
// digits of Fibonacci numbers repeats after 60.
#include <stdio.h>
#define max 100
int main()
{
long long int arr[max];
arr[0] = 0;
arr[1] = 1;
int i = 0;
// storing Fibonacci numbers
for (i = 2; i < max; i++)
arr[i] = arr[i - 1] + arr[i - 2];
// Traversing through store numbers
for (i = 1; i < max - 1; i++)
{
// Since first two number are 0 and 1
// so, if any two consecutive number encounter 0 and
// 1 at their unit place, then it clearly means that
// number is repeating/ since we just have to find
// the sum of previous two number
if ((arr[i] % 10 == 0) && (arr[i + 1] % 10 == 1))
break;
}
printf("Sequence is repeating after index %d", i);
}
// The code is contributed by Gautam goel (gautamgoel962)
Java
// Java program to demonstrate that sequence of last
// digits of Fibonacci numbers repeats after 60.
class GFG{
static int max=100;
public static void main(String[] args)
{
long[] arr=new long[max];
arr[0] = 0;
arr[1] = 1;
int i=0;
// storing Fibonacci numbers
for (i = 2; i < max; i++)
arr[i] = arr[i-1] + arr[i-2];
// Traversing through store numbers
for (i = 1; i < max - 1; i++)
{
// Since first two number are 0 and 1
// so, if any two consecutive number encounter 0 and 1
// at their unit place, then it clearly means that
// number is repeating/ since we just have to find
// the sum of previous two number
if ((arr[i] % 10 == 0) && (arr[i+1] % 10 == 1))
break;
}
System.out.println("Sequence is repeating after index "+i);
}
}
// This code is contributed by mits
Python3
# Python3 program to demonstrate that sequence of last
# digits of Fibonacci numbers repeats after 60.
if __name__=='__main__':
max = 100
arr = [0 for i in range(max)]
arr[0] = 0
arr[1] = 1
# storing Fibonacci numbers
for i in range(2, max):
arr[i] = arr[i - 1] + arr[i - 2]
# Traversing through store numbers
for i in range(1, max - 1):
# Since first two number are 0 and 1
# so, if any two consecutive number encounter 0 and 1
# at their unit place, then it clearly means that
# number is repeating/ since we just have to find
# the sum of previous two number
if((arr[i] % 10 == 0) and (arr[i + 1] % 10 == 1)):
break
print("Sequence is repeating after index", i)
# This code is contributed by
# Sanjit_Prasad
C#
// C# program to demonstrate that sequence of last
// digits of Fibonacci numbers repeats after 60.
class GFG{
static int max=100;
public static void Main()
{
long[] arr=new long[max];
arr[0] = 0;
arr[1] = 1;
int i=0;
// storing Fibonacci numbers
for (i = 2; i < max; i++)
arr[i] = arr[i-1] + arr[i-2];
// Traversing through store numbers
for (i = 1; i < max - 1; i++)
{
// Since first two number are 0 and 1
// so, if any two consecutive number encounter 0 and 1
// at their unit place, then it clearly means that
// number is repeating/ since we just have to find
// the sum of previous two number
if ((arr[i] % 10 == 0) && (arr[i+1] % 10 == 1))
break;
}
System.Console.WriteLine("Sequence is repeating after index "+i);
}
}
// This code is contributed by mits
PHP
<?php
// php program to demonstrate that
// sequence of last digits of
// Fibonacci numbers repeats after
// 60. global $MAX=100
$arr[0] = 0;
$arr[1] = 1;
// storing Fibonacci numbers
for ($i = 2; $i < 100; $i++)
$arr[$i] = $arr[$i-1] +
$arr[$i-2];
// Traversing through store
// numbers
for ($i = 1; $i <100 - 1; $i++)
{
// Since first two number are
// 0 and 1 so, if any two
// consecutive number encounter
// 0 and 1 at their unit place,
// then it clearly means that
// number is repeating/ since
// we just have to find the
// sum of previous two number
if (($arr[$i] % 10 == 0) &&
($arr[$i+1] % 10 == 1))
break;
}
echo "Sequence is repeating after",
" index ", $i;
// This code is contributed by ajit
?>
Javascript
<script>
// Javascript program to demonstrate that
// sequence of last digits of Fibonacci
// numbers repeats after 60.
var max = 100;
var arr = Array(max).fill(0);
arr[0] = 0;
arr[1] = 1;
var i = 0;
// Storing Fibonacci numbers
for(i = 2; i < max; i++)
arr[i] = arr[i - 1] + arr[i - 2];
// Traversing through store numbers
for(i = 1; i < max - 1; i++)
{
// Since first two number are 0 and 1
// so, if any two consecutive number encounter 0 and 1
// at their unit place, then it clearly means that
// number is repeating since we just have to find
// the sum of previous two number
if ((arr[i] % 10 == 0) && (arr[i + 1] % 10 == 1))
break;
}
// Driver code
document.write("Sequence is repeating after index " + i);
// This code is contributed by gauravrajput1
</script>
Producción:
Sequence is repeating after index 60
2. Factores del número de Fibonacci: en una observación cuidadosa, podemos observar lo siguiente:
- Cada tercer número de Fibonacci es un múltiplo de 2
- Cada 4-ésimo número de Fibonacci es un múltiplo de 3
- Cada quinto número de Fibonacci es un múltiplo de 5
- Cada sexto número de Fibonacci es un múltiplo de 8
Consulte esto para más detalles.
C++
// C++ program to demonstrate divisibility of Fibonacci
// numbers.
#include<iostream>
using namespace std;
#define MAX 90
int main()
{
// indexes variable stores index of number that
// is divisible by 2, 3, 5 and 8
long long int arr[MAX], index1[MAX], index2[MAX];
long long int index3[MAX], index4[MAX];
// storing fibonacci numbers
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i-1] + arr[i-2];
// c1 keeps track of number of index of number
// divisible by 2 and others c2, c3 and c4 for
// 3, 5 and 8
int c1 = 0, c2 = 0, c3 = 0, c4 = 0;
// separating fibonacci number into their
// respective array
for (int i = 0; i < MAX; i++)
{
if (arr[i] % 2 == 0)
index1[c1++] = i;
if (arr[i] % 3 == 0)
index2[c2++] = i;
if (arr[i] % 5 == 0)
index3[c3++] = i;
if (arr[i] % 8 == 0)
index4[c4++] = i;
}
// printing index arrays
cout<<"Index of Fibonacci numbers divisible by"
" 2 are :\n";
for (int i = 0; i < c1; i++)
cout<<" "<< index1[i];
cout<<"\n";
cout<<"Index of Fibonacci number divisible by"
" 3 are :\n";
for (int i = 0; i < c2; i++)
cout<<" "<< index2[i];
cout<<"\n";
cout<<"Index of Fibonacci number divisible by"
" 5 are :\n";
for (int i = 0; i < c3; i++)
cout<<" "<< index3[i];
cout<<"\n";
cout<<"Index of Fibonacci number divisible by"
" 8 are :\n";
for (int i = 0; i < c4; i++)
cout<<" "<<index4[i];
cout<<"\n";
}
// This code is contributed by shivanisinghss2110
C
// C program to demonstrate divisibility of Fibonacci
// numbers.
#include<stdio.h>
#define MAX 90
int main()
{
// indexes variable stores index of number that
// is divisible by 2, 3, 5 and 8
long long int arr[MAX], index1[MAX], index2[MAX];
long long int index3[MAX], index4[MAX];
// storing fibonacci numbers
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i-1] + arr[i-2];
// c1 keeps track of number of index of number
// divisible by 2 and others c2, c3 and c4 for
// 3, 5 and 8
int c1 = 0, c2 = 0, c3 = 0, c4 = 0;
// separating fibonacci number into their
// respective array
for (int i = 0; i < MAX; i++)
{
if (arr[i] % 2 == 0)
index1[c1++] = i;
if (arr[i] % 3 == 0)
index2[c2++] = i;
if (arr[i] % 5 == 0)
index3[c3++] = i;
if (arr[i] % 8 == 0)
index4[c4++] = i;
}
// printing index arrays
printf("Index of Fibonacci numbers divisible by"
" 2 are :\n");
for (int i = 0; i < c1; i++)
printf("%d ", index1[i]);
printf("\n");
printf("Index of Fibonacci number divisible by"
" 3 are :\n");
for (int i = 0; i < c2; i++)
printf("%d ", index2[i]);
printf("\n");
printf("Index of Fibonacci number divisible by"
" 5 are :\n");
for (int i = 0; i < c3; i++)
printf("%d ", index3[i]);
printf("\n");
printf("Index of Fibonacci number divisible by"
" 8 are :\n");
for (int i = 0; i < c4; i++)
printf("%d ", index4[i]);
printf("\n");
}
Java
// Java program to demonstrate divisibility of Fibonacci
// numbers.
class GFG
{
static int MAX=90;
// Driver code
public static void main(String[] args)
{
// indexes variable stores index of number that
// is divisible by 2, 3, 5 and 8
long[] arr=new long[MAX];
long[] index1=new long[MAX];
long[] index2=new long[MAX];
long[] index3=new long[MAX];
long[] index4=new long[MAX];
// storing fibonacci numbers
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i - 1] + arr[i - 2];
// c1 keeps track of number of index of number
// divisible by 2 and others c2, c3 and c4 for
// 3, 5 and 8
int c1 = 0, c2 = 0, c3 = 0, c4 = 0;
// separating fibonacci number into their
// respective array
for (int i = 0; i < MAX; i++)
{
if (arr[i] % 2 == 0)
index1[c1++] = i;
if (arr[i] % 3 == 0)
index2[c2++] = i;
if (arr[i] % 5 == 0)
index3[c3++] = i;
if (arr[i] % 8 == 0)
index4[c4++] = i;
}
// printing index arrays
System.out.print("Index of Fibonacci numbers divisible by" +
" 2 are :\n");
for (int i = 0; i < c1; i++)
System.out.print(index1[i] + " ");
System.out.print("\n");
System.out.print("Index of Fibonacci number divisible by" +
" 3 are :\n");
for (int i = 0; i < c2; i++)
System.out.print(index2[i] + " ");
System.out.print("\n");
System.out.print("Index of Fibonacci number divisible by" +
" 5 are :\n");
for (int i = 0; i < c3; i++)
System.out.print(index3[i] + " ");
System.out.print("\n");
System.out.print("Index of Fibonacci number divisible by" +
" 8 are :\n");
for (int i = 0; i < c4; i++)
System.out.print(index4[i] + " ");
System.out.print("\n");
}
}
// This code is contributed by mits
Python3
# Python3 program to demonstrate divisibility
# of Fibonacci numbers.
MAX = 90;
# indexes variable stores index of number
# that is divisible by 2, 3, 5 and 8
arr = [0] * (MAX);
index1 = [0] * (MAX);
index2 = [0] * (MAX);
index3 = [0] * (MAX);
index4 = [0] * (MAX);
# storing fibonacci numbers
arr[0] = 0;
arr[1] = 1;
for i in range(2, MAX):
arr[i] = arr[i - 1] + arr[i - 2];
# c1 keeps track of number of index
# of number divisible by 2 and others
# c2, c3 and c4 for 3, 5 and 8
c1, c2, c3, c4 = 0, 0, 0, 0;
# separating fibonacci number into
# their respective array
for i in range(MAX):
if (arr[i] % 2 == 0):
index1[c1] = i;
c1 += 1;
if (arr[i] % 3 == 0):
index2[c2] = i;
c2 += 1;
if (arr[i] % 5 == 0):
index3[c3] = i;
c3 += 1;
if (arr[i] % 8 == 0):
index4[c4] = i;
c4 += 1;
# printing index arrays
print("Index of Fibonacci numbers",
"divisible by 2 are :");
for i in range(c1):
print(index1[i], end = " ");
print("");
print("Index of Fibonacci number",
"divisible by 3 are :");
for i in range(c2):
print(index2[i], end = " ");
print("");
print("Index of Fibonacci number",
"divisible by 5 are :");
for i in range(c3):
print(index3[i], end = " ");
print("");
print("Index of Fibonacci number",
"divisible by 8 are :");
for i in range(c4):
print(index4[i], end = " ");
print("");
# This code is contributed by mits
C#
// C# program to demonstrate divisibility
// of Fibonacci numbers.
class GFG{
static int MAX = 90;
static void Main()
{
// indexes variable stores index of number that
// is divisible by 2, 3, 5 and 8
long[] arr = new long[MAX];
long[] index1 = new long[MAX];
long[] index2 = new long[MAX];
long[] index3 = new long[MAX];
long[] index4 = new long[MAX];
// storing fibonacci numbers
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i-1] + arr[i-2];
// c1 keeps track of number of index of number
// divisible by 2 and others c2, c3 and c4 for
// 3, 5 and 8
int c1 = 0, c2 = 0, c3 = 0, c4 = 0;
// separating fibonacci number into their
// respective array
for (int i = 0; i < MAX; i++)
{
if (arr[i] % 2 == 0)
index1[c1++] = i;
if (arr[i] % 3 == 0)
index2[c2++] = i;
if (arr[i] % 5 == 0)
index3[c3++] = i;
if (arr[i] % 8 == 0)
index4[c4++] = i;
}
// printing index arrays
System.Console.Write("Index of Fibonacci numbers" +
"divisible by 2 are :\n");
for (int i = 0; i < c1; i++)
System.Console.Write(index1[i]+" ");
System.Console.Write("\n");
System.Console.Write("Index of Fibonacci number "+
" divisible by 3 are :\n");
for (int i = 0; i < c2; i++)
System.Console.Write(index2[i]+" ");
System.Console.Write("\n");
System.Console.Write("Index of Fibonacci number "+
"divisible by 5 are :\n");
for (int i = 0; i < c3; i++)
System.Console.Write(index3[i]+" ");
System.Console.Write("\n");
System.Console.Write("Index of Fibonacci number "+
"divisible by 8 are :\n");
for (int i = 0; i < c4; i++)
System.Console.Write(index4[i]+" ");
System.Console.Write("\n");
}
}
// This code is contributed by mits
PHP
<?php
// PHP program to demonstrate divisibility
// of Fibonacci numbers.
$MAX = 90;
// indexes variable stores index of number
// that is divisible by 2, 3, 5 and 8
$arr = array($MAX);
$index1 = array($MAX);
$index2 = array($MAX);
$index3 = array($MAX);
$index4 = array($MAX);
// storing fibonacci numbers
$arr[0] = 0;
$arr[1] = 1;
for ($i = 2; $i < $MAX; $i++)
{
$arr[$i] = $arr[$i - 1] + $arr[$i - 2];
}
// c1 keeps track of number of index of
// number divisible by 2 and others
// c2, c3 and c4 for 3, 5 and 8
$c1 = 0;
$c2 = 0;
$c3 = 0;
$c4 = 0;
// separating fibonacci number into
// their respective array
for ($i = 0; $i < $MAX; $i++)
{
if ($arr[$i] % 2 == 0)
$index1[$c1++] = $i;
if ($arr[$i] % 3 == 0)
$index2[$c2++] = $i;
if ($arr[$i] % 5 == 0)
$index3[$c3++] = $i;
if ($arr[$i] % 8 == 0)
$index4[$c4++] = $i;
}
// printing index arrays
echo "Index of Fibonacci numbers divisible by" .
" 2 are :\n";
for ($i = 0; $i < $c1; $i++)
echo $index1[$i] . " ";
echo "\n";
echo "Index of Fibonacci number divisible by" .
" 3 are :\n";
for ($i = 0; $i < $c2; $i++)
echo $index2[$i] . " ";
echo "\n";
echo "Index of Fibonacci number divisible by" .
" 5 are :\n";
for ($i = 0; $i < $c3; $i++)
echo $index3[$i] . " ";
echo "\n";
echo "Index of Fibonacci number divisible by" .
" 8 are :\n";
for ($i = 0; $i < $c4; $i++)
echo $index4[$i] . " ";
echo "\n";
// This code is contributed by mits
?>
Javascript
// JavaScript program to demonstrate divisibility of Fibonacci
// numbers.
var MAX=90;
// Driver code
// indexes variable stores index of number that
// is divisible by 2, 3, 5 and 8
var arr=new Array(MAX);
var index1= new Array(MAX);
var index2= new Array(MAX);
var index3= new Array(MAX);
var index4= new Array(MAX);
// storing fibonacci numbers
arr[0] = 0;
arr[1] = 1;
for (var i = 2; i < MAX; i++)
arr[i] = arr[i - 1] + arr[i - 2];
// c1 keeps track of number of index of number
// divisible by 2 and others c2, c3 and c4 for
// 3, 5 and 8
var c1 = 0, c2 = 0, c3 = 0, c4 = 0;
// separating fibonacci number into their
// respective array
for (var i = 0; i < MAX; i++)
{
if (arr[i] % 2 == 0)
index1[c1++] = i;
if (arr[i] % 3 == 0)
index2[c2++] = i;
if (arr[i] % 5 == 0)
index3[c3++] = i;
if (arr[i] % 8 == 0)
index4[c4++] = i;
}
// printing index arrays
document.write("Index of Fibonacci numbers divisible by" +
" 2 are :\n");
for (var i = 0; i < c1; i++)
document.write(index1[i] + " ");
document.write("\n");
document.write("Index of Fibonacci number divisible by" +
" 3 are :\n");
for (var i = 0; i < c2; i++)
document.write(index2[i] + " ");
document.write("\n");
document.write("Index of Fibonacci number divisible by" +
" 5 are :\n");
for (var i = 0; i < c3; i++)
document.write(index3[i] + " ");
document.write("\n");
document.write("Index of Fibonacci number divisible by" +
" 8 are :\n");
for (var i = 0; i < c4; i++)
document.write(index4[i] + " ");
document.write("\n");
// This code is contributed by shivanisinghss2110
Producción:
Index of Fibonacci numbers divisible by 2 are : 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 Index of Fibonacci number divisible by 3 are : 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 Index of Fibonacci number divisible by 5 are : 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Index of Fibonacci number divisible by 8 are : 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84
3. Número de Fibonacci con factor de número índice: Tenemos un número de Fibonacci como F(1) = 1 que es divisible por 1, F(5) = 5 que es divisible por 5, F(12) = 144 que es divisible por 12 , F(24) = 46368 que es divisible por 24, F(25) = 75025 que es divisible por 25. Este tipo de número índice sigue un cierto patrón. Primero, echemos un vistazo a esos números de índice:
1, 5, 12, 24, 25, 36, 48, 60, 72, 84, 96, 108, 120, 125, 132, …..
Al observarla, esta serie está formada por todo número que sea múltiplo de 12 así como por todo número que cumpla la condición de pow(5, k), donde k = 0, 1, 2, 3, 4, 5, 6, 7, …….
C++
// C++ program to demonstrate that Fibonacci numbers
// that are divisible by their indexes have indexes
// as either power of 5 or multiple of 12.
#include<iostream>
using namespace std;
#define MAX 100
int main()
{
// storing Fibonacci numbers
long long int arr[MAX];
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i-1] + arr[i-2];
cout<<"Fibonacci numbers divisible by "
"their indexes are :\n";
for (int i = 1; i < MAX; i++)
if (arr[i] % i == 0)
cout<<" "<< i;
}
// This code is contributed by shivanisinghss2110
C
// C program to demonstrate that Fibonacci numbers
// that are divisible by their indexes have indexes
// as either power of 5 or multiple of 12.
#include<stdio.h>
#define MAX 100
int main()
{
// storing Fibonacci numbers
long long int arr[MAX];
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i-1] + arr[i-2];
printf("Fibonacci numbers divisible by "
"their indexes are :\n");
for (int i = 1; i < MAX; i++)
if (arr[i] % i == 0)
printf("%d ", i);
}
Java
// Java program to demonstrate that Fibonacci numbers
// that are divisible by their indexes have indexes
// as either power of 5 or multiple of 12.
class GFG
{
static int MAX = 100;
public static void main(String[] args)
{
// storing Fibonacci numbers
long[] arr = new long[MAX];
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i - 1] + arr[i - 2];
System.out.print("Fibonacci numbers divisible by "+
"their indexes are :\n");
for (int i = 1; i < MAX; i++)
if (arr[i] % i == 0)
System.out.print(i + " ");
}
}
// This code is contributed by mits
Python3
# Python3 program to demonstrate that Fibonacci numbers
# that are divisible by their indexes have indexes
# as either power of 5 or multiple of 12.
if __name__=='__main__':
MAX = 100
# storing Fibonacci numbers
arr = [0 for i in range(MAX)]
arr[0] = 0
arr[1] = 1
for i in range(2, MAX):
arr[i] = arr[i - 1] + arr[i - 2]
print("Fibonacci numbers divisible by their indexes are :")
for i in range(1, MAX):
if(arr[i] % i == 0):
print(i,end=" ")
# This code is contributed by
# Sanjit_Prasad
C#
// C# program to demonstrate that Fibonacci
// numbers that are divisible by their
// indexes have indexes as either power of 5
// or multiple of 12.
using System;
class GFG
{
static int MAX = 100;
static void Main()
{
// storing Fibonacci numbers
long[] arr = new long[MAX];
arr[0] = 0;
arr[1] = 1;
for (int i = 2; i < MAX; i++)
arr[i] = arr[i - 1] + arr[i - 2];
Console.Write("Fibonacci numbers divisible by " +
"their indexes are :\n");
for (int i = 1; i < MAX; i++)
if (arr[i] % i == 0)
System.Console.Write(i+" ");
}
}
// This code is contributed by mits
Javascript
// JavaScript program to demonstrate that Fibonacci numbers
// that are divisible by their indexes have indexes
// as either power of 5 or multiple of 12.
var MAX = 100;
// storing Fibonacci numbers
var arr = new Array(MAX);
arr[0] = 0;
arr[1] = 1;
for (var i = 2; i < MAX; i++)
arr[i] = arr[i - 1] + arr[i - 2];
document.write("Fibonacci numbers divisible by their indexes are :");
for (var i = 1; i < MAX; i++)
if (arr[i] % i == 0)
document.write(i + " ");
// This code is contributed by shivanisinghss2110
Producción:
Fibonacci numbers divisible by their indexes are : 1 5 12 24 25 36 48 60 72 96
4. El valor de f(n-1)*f(n+1) – f(n)*f(n) es (-1) n . Consulte la Identidad de Cassini para obtener más detalles.
Referencia:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html
Este artículo es una contribución de Aditya Kumar . Si le gusta GeeksforGeeks y le gustaría contribuir, también puede escribir un artículo usando contribuya.geeksforgeeks.org o envíe su artículo por correo a review-team@geeksforgeeks.org. Vea su artículo que aparece en la página principal de GeeksforGeeks y ayude a otros Geeks.
Escriba comentarios si encuentra algo incorrecto o si desea compartir más información sobre el tema tratado anteriormente.
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA