SOLUTION: The FIbonacci numbers f_n are defined by the equations f_1 = 1, f_2 = 1, f_(n+1) = f_n + f_(n−1) (n ≥ 2). Find gcd(f_10,7!)

Algebra.Com
Question 1033751: The FIbonacci numbers f_n are defined by the equations f_1 = 1, f_2 = 1,
f_(n+1) = f_n + f_(n−1) (n ≥ 2).
Find gcd(f_10,7!)
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
The FIbonacci numbers f_n are defined by the equations f_1 = 1, f_2 = 1,
f_(n+1) = f_n + f_(n−1) (n ≥ 2).
Find gcd(f_10,7!)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

I made calculations and got  = 55.


Hence,  gcd(f_10,7!) = 5.

When I completed it, I looked into Wikipedia (this article).

It confirms that = 55.

So you can replace calculations by looking in Wikipedia, too.


RELATED QUESTIONS

Let {F(n)} = {1,1,2,3,5,8,13,21,34,55,···} be the Fibonacci sequence defined by F(1) = (answered by AnlytcPhil)
The Fibonacci sequence, is defined by F_0 = 0, F_1 = 1, and F_n = F_{n - 2} + F_{n - 1}. (answered by CPhill,greenestamps)
Let (Fn)=(1,1,2,3,5,8,13,21,34,55,...) be the fibonacci sequence defined by F1=F2=1,... (answered by venugopalramana)
given f(n) = 1/2 n + 1; find... (answered by ikleyn)
The Fibonacci numbers f_n are defined by the equations f_1 = 1, f_2 = 1, f_(n+1) =f_n +... (answered by ikleyn)
If f(1) = 7 and f(n) = f(n - 1) + 2 then find the value of... (answered by ikleyn)
The function f(n) is defined for all integers n, such that f(x) + f(y) = f(x + y) -... (answered by CPhill,ikleyn)
Let f be a function defined by f(n)=2f(n-1)+3f(n-2), where f(1)=3 and f(2) = 1.... (answered by ikleyn)
A sequence has its first term equal to 4, and each term of the sequence is obtained by... (answered by ikleyn)