{
  "status": "PASS",
  "arithmetic": "integer and Fraction only",
  "checks": {
    "gaussian_gcd_29_12_plus_i": {
      "gcd": [
        5,
        -2
      ],
      "bezout": [
        [
          1,
          0
        ],
        [
          -2,
          0
        ]
      ],
      "trace": [
        {
          "a": [
            29,
            0
          ],
          "b": [
            12,
            1
          ],
          "q": [
            2,
            0
          ],
          "r": [
            5,
            -2
          ]
        },
        {
          "a": [
            12,
            1
          ],
          "b": [
            5,
            -2
          ],
          "q": [
            2,
            1
          ],
          "r": [
            0,
            0
          ]
        }
      ]
    },
    "gaussian_grid_gcd_cases": 2400,
    "quotient_kernel_cases": 3721,
    "count_formula_n_range": [
      1,
      3000
    ],
    "325": {
      "r2": 24,
      "primitive_r2": 16,
      "positive_unordered": [
        [
          1,
          18
        ],
        [
          6,
          17
        ],
        [
          10,
          15
        ]
      ],
      "primitive_pairs": [
        [
          1,
          18
        ],
        [
          6,
          17
        ]
      ],
      "all_signed_ordered": [
        [
          -18,
          -1
        ],
        [
          -18,
          1
        ],
        [
          -17,
          -6
        ],
        [
          -17,
          6
        ],
        [
          -15,
          -10
        ],
        [
          -15,
          10
        ],
        [
          -10,
          -15
        ],
        [
          -10,
          15
        ],
        [
          -6,
          -17
        ],
        [
          -6,
          17
        ],
        [
          -1,
          -18
        ],
        [
          -1,
          18
        ],
        [
          1,
          -18
        ],
        [
          1,
          18
        ],
        [
          6,
          -17
        ],
        [
          6,
          17
        ],
        [
          10,
          -15
        ],
        [
          10,
          15
        ],
        [
          15,
          -10
        ],
        [
          15,
          10
        ],
        [
          17,
          -6
        ],
        [
          17,
          6
        ],
        [
          18,
          -1
        ],
        [
          18,
          1
        ]
      ]
    },
    "cornacchia_all_root_cases": 478,
    "cornacchia_moduli_range": [
      2,
      2000
    ],
    "cornacchia_325": {
      "18": {
        "answer": [
          18,
          1
        ],
        "trace": [
          {
            "j": 0,
            "r": 325,
            "s": 0
          },
          {
            "j": 1,
            "r": 18,
            "s": 1
          }
        ]
      },
      "57": {
        "answer": [
          17,
          6
        ],
        "trace": [
          {
            "j": 0,
            "r": 325,
            "s": 0
          },
          {
            "j": 1,
            "r": 57,
            "s": 1
          },
          {
            "j": 2,
            "r": 40,
            "s": 5,
            "q": 5
          },
          {
            "j": 3,
            "r": 17,
            "s": 6,
            "q": 1
          }
        ]
      }
    },
    "roots_minus_one_mod_325": [
      18,
      57,
      268,
      307
    ],
    "primitive_triples_c_le_500": 80,
    "primitive_triples_c_325": [
      [
        253,
        204,
        325
      ],
      [
        323,
        36,
        325
      ]
    ],
    "rational_circle_exact_cases": 820,
    "rejected_invalid_inputs": 7,
    "mutated_stop_and_coefficient_rejected": 2,
    "general_d_counterexample": {
      "d": 5,
      "m": 7,
      "root": 3,
      "terminal_r": 1,
      "terminal_s": 2,
      "weighted_norm": 21
    }
  }
}