class Integer
  def mod_exp(exp, mod)
    exp < 0 and raise ArgumentError, "negative exponent"
    prod = 1
    base = self % mod
    until exp.zero?
      exp.odd? and prod = (prod * base) % mod
      exp >>= 1
      base = (base * base) % mod
    end
    prod
  end
end

PHI = (1 + Math.sqrt(5)) / 2

def fib(n)
  ((PHI ** n - (-1 / PHI) ** n) / Math.sqrt(5)).to_i
end

puts fib(8)