Solve some problems.

python/e138.py

@@ -0,0 +1,32 @@
+from math import gcd
+
+
+def euler_138():
+    count = 12
+    r, m, n = 0, 2, 1
+    while True:
+        if count == 0:
+            break
+
+        if (m - n) % 2 == 1 and gcd(m, n) == 1:  # Ensure m and n are coprime and not both odd
+            a = m * m - n * n
+            b = 2 * m * n
+            c = m * m + n * n
+            if a > b:
+                a, b = b, a
+            assert a * a + b * b == c * c
+            if a * 2 - 1 == b or a * 2 + 1 == b:
+                # print(f"{m=} {n=} l={c}")
+                r += c # c is L
+                count -= 1
+                n = m
+                m *= 4
+        m += 1
+    return r
+
+
+if __name__ == "__main__":
+    solution = euler_138()
+    print("e138.py: " + str(solution))
+    assert solution == 1118049290473932
+