Replace assert-based validation with explicit errors in modular_division (#14204)

* Improve documentation for linear search algorithm

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* Replace asserts with explicit validation in modular_division

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

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

* Update linear_search.py

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Co-authored-by: Anusha-DeviE <itzanushadevi@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Author: 4 people

maths/modular_division.py

@@ -28,9 +28,13 @@ def modular_division(a: int, b: int, n: int) -> int:
     4
 
     """
-    assert n > 1
-    assert a > 0
-    assert greatest_common_divisor(a, n) == 1
+    if n <= 1:
+        raise ValueError("Modulus n must be greater than 1")
+    if a <= 0:
+        raise ValueError("Divisor a must be a positive integer")
+    if greatest_common_divisor(a, n) != 1:
+        raise ValueError("a and n must be coprime (gcd(a, n) = 1)")
+
     (_d, _t, s) = extended_gcd(n, a)  # Implemented below
     x = (b * s) % n
     return x