/* 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