From 2289014984dd2c69f0d507799fd3427c8816a33f Mon Sep 17 00:00:00 2001
From: zhk319 <3680097025@qq.com>
Date: Wed, 27 May 2026 10:12:55 +0800
Subject: [PATCH 1/3] feat: add Lucas numbers algorithm with doctests

---
 maths/lucas_numbers.py | 39 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 maths/lucas_numbers.py

diff --git a/maths/lucas_numbers.py b/maths/lucas_numbers.py
new file mode 100644
index 000000000000..ff34627655c0
--- /dev/null
+++ b/maths/lucas_numbers.py
@@ -0,0 +1,39 @@
+def lucas_number(n: int) -> int:
+    """
+    Returns the n-th Lucas number using an iterative approach.
+    The Lucas numbers are an integer sequence where each term is the sum of the
+    two preceding terms, starting with 2 and 1.
+
+    Reference: https://en.wikipedia.org/wiki/Lucas_number
+
+    >>> lucas_number(0)
+    2
+    >>> lucas_number(1)
+    1
+    >>> lucas_number(5)
+    11
+    >>> lucas_number(10)
+    123
+    >>> lucas_number(-3)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be a non-negative integer.
+    """
+    if n < 0:
+        raise ValueError("n must be a non-negative integer.")
+
+    if n == 0:
+        return 2
+    if n == 1:
+        return 1
+
+    a, b = 2, 1
+    for _ in range(2, n + 1):
+        a, b = b, a + b
+    return b
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
\ No newline at end of file

From f41ca6a15fe079a7d01210665d15d8e3a761c37d Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 27 May 2026 02:16:44 +0000
Subject: [PATCH 2/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/lucas_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/lucas_numbers.py b/maths/lucas_numbers.py
index ff34627655c0..0ebfc5d8a6e9 100644
--- a/maths/lucas_numbers.py
+++ b/maths/lucas_numbers.py
@@ -36,4 +36,4 @@ def lucas_number(n: int) -> int:
 if __name__ == "__main__":
     import doctest
 
-    doctest.testmod()
\ No newline at end of file
+    doctest.testmod()

From b366d52ac2fa83b3b3555b9f52bc57260a1bd585 Mon Sep 17 00:00:00 2001
From: zhk319 <3680097025@qq.com>
Date: Wed, 27 May 2026 10:33:07 +0800
Subject: [PATCH 3/3] fix: change parameter name to a descriptive word to
 satisfy bot

---
 maths/lucas_numbers.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/maths/lucas_numbers.py b/maths/lucas_numbers.py
index ff34627655c0..90bc7168fbda 100644
--- a/maths/lucas_numbers.py
+++ b/maths/lucas_numbers.py
@@ -1,4 +1,4 @@
-def lucas_number(n: int) -> int:
+def lucas_number(input_index: int) -> int:
     """
     Returns the n-th Lucas number using an iterative approach.
     The Lucas numbers are an integer sequence where each term is the sum of the
@@ -17,18 +17,18 @@ def lucas_number(n: int) -> int:
     >>> lucas_number(-3)
     Traceback (most recent call last):
         ...
-    ValueError: n must be a non-negative integer.
+    ValueError: input_index must be a non-negative integer.
     """
-    if n < 0:
-        raise ValueError("n must be a non-negative integer.")
+    if input_index < 0:
+        raise ValueError("input_index must be a non-negative integer.")
 
-    if n == 0:
+    if input_index == 0:
         return 2
-    if n == 1:
+    if input_index == 1:
         return 1
 
     a, b = 2, 1
-    for _ in range(2, n + 1):
+    for _ in range(2, input_index + 1):
         a, b = b, a + b
     return b