Solve some problems.

python/e139.py

@@ -0,0 +1,35 @@
+from math import gcd
+
+
+def euler_139():
+    limit = 100_000_000
+    r, m, n = 0, 2, 1
+    while True:
+        a = m * m - 1 * 1
+        b = 2 * m * 1
+        c = m * m + 1 * 1
+        if a + b + c > limit:
+            return r
+
+        for n in range(1, m):
+            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
+
+                ka, kb, kc = a, b, c 
+                while ka + kb + kc < limit:
+                    assert ka * ka + kb * kb == kc * kc
+                    if kc % (kb - ka) == 0:
+                        r += 1
+                    ka, kb, kc = ka + a, kb + b, kc + c
+        m += 1
+
+
+if __name__ == "__main__":
+    solution = euler_139()
+    print("e139.py: " + str(solution))
+    assert solution == 10057761
+