code: def test_euler_pseudoprimes():
      assert is_euler_pseudoprime(13, 1)
      assert is_euler_pseudoprime(15, 1)
      assert is_euler_pseudoprime(17, 6)
      assert is_euler_pseudoprime(101, 7)
      assert is_euler_pseudoprime(1009, 10)
      assert is_euler_pseudoprime(11287, 41)
  
      raises(ValueError, lambda: is_euler_pseudoprime(0, 4))
      raises(ValueError, lambda: is_euler_pseudoprime(3, 0))
      raises(ValueError, lambda: is_euler_pseudoprime(15, 6))
  
      # A006970
      euler_prp = [
          341,
          561,
          1105,
          1729,
          1905,
          2047,
          2465,
          3277,
          4033,
          4681,
          5461,
          6601,
          8321,
          8481,
          10261,
          10585,
      ]
      for p in euler_prp:
          assert is_euler_pseudoprime(p, 2)
  
      # A048950
      euler_prp = [
          121,
          703,
          1729,
          1891,
          2821,
          3281,
          7381,
          8401,
          8911,
          10585,
          12403,
          15457,
          15841,
          16531,
          18721,
          19345,
          23521,
          24661,
          28009,
      ]
      for p in euler_prp:
          assert is_euler_pseudoprime(p, 3)
  
      # A033181
      absolute_euler_prp = [
          1729,
          2465,
          15841,
          41041,
          46657,
          75361,
          162401,
          172081,
          399001,
          449065,
          488881,
      ]
      for p in absolute_euler_prp:
          for a in range(2, p):
              if gcd(a, p) != 1:
                  continue
              assert is_euler_pseudoprime(p, a)
  
file_path: sympy/sympy/ntheory/tests/test_primetest.py
imports: from math import gcd
  from sympy.ntheory.generate import Sieve, sieve
  from sympy.ntheory.primetest import mr, _lucas_extrastrong_params, is_lucas_prp, is_square, is_strong_lucas_prp, is_extra_strong_lucas_prp, proth_test, isprime, is_euler_pseudoprime, is_gaussian_prime, is_fermat_pseudoprime, is_euler_jacobi_pseudoprime, MERSENNE_PRIME_EXPONENTS, _lucas_lehmer_primality_test, is_mersenne_prime
  from sympy.testing.pytest import slow, raises
  from sympy.core.numbers import I
label_desc: Use image node_id 2 for calling a global function with example usage: test_euler_pseudoprimes() without return types