Thank you for voting the question. My reputation is above 10 so I can post it rigth now :). I've got a pretty simple solution using the package gmp (a library mentioned as well in the link provided by Ben Bolker) to sum large integers.
require(gmp)
fib <- function(n) {
a = 0
b = 1
for (i in 1:n) {
tmp = b
b = a
a = add.bigz(a, tmp) # gmp function
}
return (a)
}
fib(79)
The result is the right Fibonacci number, fib(79): 14472334024676221. I tested it for even larger integers fib(5000), 1045 digits, and the result seems accurate to the last digit.