code: def test_bf_pell():
      assert diop_bf_DN(13, -4) == [(3, 1), (-3, 1), (36, 10)]
      assert diop_bf_DN(13, 27) == [
          (12, 3),
          (-12, 3),
          (40, 11),
          (-40, 11),
      ]
      assert diop_bf_DN(167, -2) == []
      assert diop_bf_DN(1729, 1) == [(44611924489705, 1072885712316)]
      assert diop_bf_DN(89, -8) == [(9, 1), (-9, 1)]
      assert diop_bf_DN(21257, -1) == [(13913102721304, 95427381109)]
      assert diop_bf_DN(340, -4) == [(756, 41)]
      assert diop_bf_DN(-1, 0, t) == [(0, 0)]
      assert diop_bf_DN(0, 0, t) == [(0, t)]
      assert diop_bf_DN(4, 0, t) == [(2 * t, t), (-2 * t, t)]
      assert diop_bf_DN(3, 0, t) == [(0, 0)]
      assert diop_bf_DN(1, -2, t) == []
  
imports: from sympy.core.add import Add
  from sympy.core.mul import Mul
  from sympy.core.numbers import Rational, oo, pi
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.matrices.dense import Matrix
  from sympy.ntheory.factor_ import factorint
  from sympy.simplify.powsimp import powsimp
  from sympy.core.function import _mexpand
  from sympy.core.sorting import default_sort_key, ordered
  from sympy.functions.elementary.trigonometric import sin
  from sympy.solvers.diophantine import diophantine
  from sympy.solvers.diophantine.diophantine import diop_DN, diop_solve, diop_ternary_quadratic_normal, diop_general_pythagorean, diop_ternary_quadratic, diop_linear, diop_quadratic, diop_general_sum_of_squares, diop_general_sum_of_even_powers, descent, diop_bf_DN, divisible, equivalent, find_DN, ldescent, length, reconstruct, partition, power_representation, prime_as_sum_of_two_squares, square_factor, sum_of_four_squares, sum_of_three_squares, transformation_to_DN, transformation_to_normal, classify_diop, base_solution_linear, cornacchia, sqf_normal, gaussian_reduce, holzer, check_param, parametrize_ternary_quadratic, sum_of_powers, sum_of_squares, _diop_ternary_quadratic_normal, _nint_or_floor, _odd, _even, _remove_gcd, _can_do_sum_of_squares, DiophantineSolutionSet, GeneralPythagorean, BinaryQuadratic
  from sympy.testing.pytest import slow, raises, XFAIL
  from sympy.utilities.iterables import signed_permutations
label_desc: Use image node_id 16 for calling a global function with example usage: test_bf_pell() without return types