code: def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
         if not isinstance(lowercase_		,						lowercase_				):
                raise TypeError('recursive_lucas_number accepts only integer arguments.'				)
         if n_th_number == 0:
                return 2
         if n_th_number == 1:
                return 1
  
         return recursive_lucas_number(n_th_number - 1				) + recursive_lucas_number(
             n_th_number - 2				)
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	int				):
         if not isinstance(lowercase_		,						lowercase_				):
                raise TypeError('dynamic_lucas_number accepts only integer arguments.'				)
         _UpperCamelCase						,      _UpperCamelCase     :       List[str]  						=  2, 1
         for _ in range(lowercase_				):
                _UpperCamelCase						,      _UpperCamelCase     :       Optional[int]  						=  b, a + b
         return a
  
  
  if __name__ == "__main__":
   from doctest import testmod
  
   testmod()
   UpperCAmelCase					=				int(input('''Enter the number of terms in lucas series:\n''').strip())
   print('''Using recursive function to calculate lucas series:''')
   print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
   print('''\nUsing dynamic function to calculate lucas series:''')
   print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))
  
  
  
  
style_context: from __future__ import annotations
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	int		,						lowercase_:	int		,						lowercase_:	int				):
         assert (
             c % greatest_common_divisor(lowercase_		,						lowercase_				) == 0
         )  # greatest_common_divisor(a,b) function implemented below
         ((_UpperCamelCase)						,      (_UpperCamelCase)						,      (_UpperCamelCase))     :       int  						=  extended_gcd(lowercase_		,						lowercase_				)  # extended_gcd(a,b) function implemented below
         _UpperCamelCase     :       List[Any]  						=  c / d
         return (r * x, r * y)
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	int		,						lowercase_:	int		,						lowercase_:	int		,						lowercase_:	int = 2				):
         ((_UpperCamelCase)						,      (_UpperCamelCase))     :       Tuple  						=  diophantine(lowercase_		,						lowercase_		,						lowercase_				)  # Initial value
         _UpperCamelCase     :       List[Any]  						=  greatest_common_divisor(lowercase_		,						lowercase_				)
         _UpperCamelCase     :       Optional[int]  						=  a // d
         _UpperCamelCase     :       Optional[Any]  						=  b // d
  
         for i in range(lowercase_				):
                _UpperCamelCase     :       Union[str, Any]  						=  xa + i * q
                _UpperCamelCase     :       List[Any]  						=  ya - i * p
                print(lowercase_		,						lowercase_				)
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	int		,						lowercase_:	int				):
         if a < b:
                _UpperCamelCase						,      _UpperCamelCase     :       Optional[Any]  						=  b, a
  
         while a % b != 0:
                _UpperCamelCase						,      _UpperCamelCase     :       Union[str, Any]  						=  b, a % b
  
         return b
  
  
  def SCREAMING_SNAKE_CASE				(     lowercase_:	int		,						lowercase_:	int				):
         assert a >= 0 and b >= 0
  
         if b == 0:
                _UpperCamelCase						,      _UpperCamelCase						,      _UpperCamelCase     :       Optional[Any]  						=  a, 1, 0
         else:
                ((_UpperCamelCase)						,      (_UpperCamelCase)						,      (_UpperCamelCase))     :       Any  						=  extended_gcd(lowercase_		,						a % b				)
                _UpperCamelCase     :       Any  						=  q
                _UpperCamelCase     :       str  						=  p - q * (a // b)
  
         assert a % d == 0 and b % d == 0
         assert d == a * x + b * y
  
         return (d, x, y)
  
  
  if __name__ == "__main__":
   from doctest import testmod
  
   testmod(name='''diophantine''', verbose=True)
   testmod(name='''diophantine_all_soln''', verbose=True)
   testmod(name='''extended_gcd''', verbose=True)
   testmod(name='''greatest_common_divisor''', verbose=True)
  
  
  
  