feat: Add automorphic number implementation (#7978)

* feat: Add automorphic number implementation

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* refactor: Add type checking for number

* refactor: Rename variable n to number

* test: Add doctest

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* test: Add unit  test for number=0

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maths/automorphic_number.py

@@ -0,0 +1,58 @@
+"""
+== Automorphic Numbers ==
+A number n is said to be a Automorphic number if
+the square of n "ends" in the same digits as n itself.
+
+Examples of Automorphic Numbers: 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, ...
+https://en.wikipedia.org/wiki/Automorphic_number
+"""
+
+# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
+# Time Complexity : O(log10n)
+
+
+def is_automorphic_number(number: int) -> bool:
+    """
+    # doctest: +NORMALIZE_WHITESPACE
+    This functions takes an integer number as input.
+    returns True if the number is automorphic.
+    >>> is_automorphic_number(-1)
+    False
+    >>> is_automorphic_number(0)
+    True
+    >>> is_automorphic_number(5)
+    True
+    >>> is_automorphic_number(6)
+    True
+    >>> is_automorphic_number(7)
+    False
+    >>> is_automorphic_number(25)
+    True
+    >>> is_automorphic_number(259918212890625)
+    True
+    >>> is_automorphic_number(259918212890636)
+    False
+    >>> is_automorphic_number(740081787109376)
+    True
+    >>> is_automorphic_number(5.0)
+    Traceback (most recent call last):
+        ...
+    TypeError: Input value of [number=5.0] must be an integer
+    """
+    if not isinstance(number, int):
+        raise TypeError(f"Input value of [number={number}] must be an integer")
+    if number < 0:
+        return False
+    number_square = number * number
+    while number > 0:
+        if number % 10 != number_square % 10:
+            return False
+        number //= 10
+        number_square //= 10
+    return True
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()