Solve problem 142 and make 141 brute force work again.

python/e142.py

@@ -0,0 +1,38 @@
+from math import isqrt
+
+
+def iq(n):
+    isq = isqrt(n)
+    return isq * isq == n
+
+
+def euler_142():
+    # x + y x - y x + z x - z y + z y - z
+    NMAX = 1_000_000
+    squares = [n * n for n in range(1, NMAX)]
+    for x in range(1, NMAX):
+        for s1 in squares:
+            y = x - s1 # s1 = x - y
+            if y <= 0:
+                break
+            if not iq(x + y): # s2 = x + y
+                continue
+            for s3 in squares:
+                z = y - s3 # s3 = y - z
+                if x - z <= 0:
+                    continue
+                if z <= 0:
+                    break
+                if not iq(y + z): # s4 = y + z
+                    continue
+                if iq(x + z) and iq(x - z):
+                    print(x, y, z, x + y + z)
+                    return x + y + z
+    return None
+
+
+if __name__ == "__main__":
+    solution = euler_142()
+    print("e142.py: " + str(solution))
+    assert solution == 1006193
+