Improvements for Fermat

kryptools/factor_fmt.py

@@ -7,6 +7,8 @@
 
 def factor_fermat(n: int, maxsteps: int|None = None, verbose: int = 0) -> list:
     """Find factors of n using the method of Fermat."""
+    if not isinstance(n, int) or n < 1:
+        raise ValueError("Number to be factored must be a positive integer!")
     if verbose:
         print(f"Factoring (Fermat): {n} ({floor(log10(n)) + 1} digits)")
     factors = []
@@ -19,6 +21,8 @@ def factor_fermat(n: int, maxsteps: int|None = None, verbose: int = 0) -> list:
         while n % p == 0:
             factors.append(p)
             n //= p
+    if n == 1:
+        return factors
     start = isqrt(n - 1) + 1
     step, mod = parameters[n % 24]
     start += (mod - start) % step

tests/test_factor_fmt.py

@@ -0,0 +1,12 @@
+import pytest
+from math import prod
+from kryptools import is_prime
+from kryptools.factor_fmt import factor_fermat
+
+
+def test_fermat():
+	for n in range(1,1000):
+		factors = factor_fermat(n)
+		assert n == prod(factors)
+		if len(factors) == 1:
+			assert is_prime(n)