Implements the euclidean and extended euclidean division algorithms

imp/math/numbertheory.py

@@ -0,0 +1,21 @@
+def euclidean_algo(a: int, b: int) -> int:
+    while b: a, b = b, a % b
+    return a
+
+'''
+Calculates coefficients x and y of Bezout's identity: ax + by = gcd(a,b)  
+NOTE: Based on the Extended Euclidean Algorithm's Wikipedia page
+'''
+def extended_euclid_algo(a: int, b: int) -> tuple[int, int]:
+    (old_r, r) = (a, b)
+    (old_s, s) = (1, 0)
+    (old_t, t) = (0, 1)
+    while r != 0:
+        q = old_r // r
+        (old_r, r) = (r, old_r - q*r)
+        (old_s, s) = (s, old_s - q*s)
+        (old_t, t) = (t, old_t - q*t)
+    # Bezout cofficients:     (old_s, old_t)
+    # Greatest Common Divisor: old_r
+    # Quotients by the gcd:   (t, s)
+    return (t, s)