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Task/Babbage-problem/NetRexx/babbage-problem.netrexx

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+/* NetRexx */
+options replace format comments java crossref symbols nobinary utf8
+numeric digits 5000 -- set up numeric precision
+
+babbageNr = babbage() -- call a function to perform the analysis and capture the result
+babbageSq = babbageNr ** 2  -- calculate the square of the result
+-- display results using a library function
+System.out.printf("%,10d\u00b2 == %,12d%n", [Integer(babbageNr), Integer(babbageSq)])
+return
+
+-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+-- A function method to answer Babbage's question:
+--   "What is the smallest positive integer whose square ends in the digits 269,696?"
+--     — Babbage, letter to Lord Bowden, 1837;
+--       see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
+--   (He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.)
+
+method babbage() public static binary
+  n = int 104 -- (integer arithmatic)
+  -- begin a processing loop to determine the value
+  -- starting point: 104
+  loop while ((n * n) // 1000000) \= 269696
+    -- loop continues while the remainder of n squared divided by 1,000,000 is not equal to 269,696
+    if n // 10 == 4 then do
+      -- increment n by 2 if the remainder of n divided by 10 equals 4
+      n = n + 2
+      end
+    if n // 10 == 6 then do
+      -- increment n by 8 if the remainder of n divided by 10 equals 6
+      n = n + 8
+      end
+    end
+
+  return n -- end the function and return the result