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Ingy döt Net 2026-02-01 16:33:20 -08:00
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54
Task/Babbage-problem/Ada/babbage-problem.ada
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-- The program is written in the programming language Ada. The name "Ada"
-- has been chosen in honour of your friend,
-- Augusta Ada King-Noel, Countess of Lovelace (née Byron).
--
-- This is an program to search for the smallest integer X, such that
-- (X*X) mod 1_000_000 = 269_696.
--
-- In the Ada language, "*" represents the multiplication symbol, "mod" the
-- modulo reduction, and the underscore "_" after every third digit in
-- literals is supposed to simplify reading numbers for humans.
-- Everything written after "--" in a line is a comment for the human,
-- and will be ignored by the computer.
with Ada.Text_IO;
-- We need this to tell the computer how it will later output its result.
procedure Babbage_Problem is
-- We know that 99_736*99_736 is 9_947_269_696. This implies:
-- 1. The smallest X with X*X mod 1_000_000 = 269_696 is at most 99_736.
-- 2. The largest square X*X, which the program may have to deal with,
-- will be at most 9_947_269_69.
type Number is range 1 .. 99_736*99_736;
X: Number := 1;
-- X can store numbers between 1 and 99_736*99_736. Computations
-- involving X can handle intermediate results in that range.
-- Initially the value stored at X is 1.
-- When running the program, the value will become 2, 3, 4, etc.
begin
-- The program starts running.
-- The computer first squares X, then it truncates the square, such
-- that the result is a six-digit number.
-- Finally, the computer checks if this number is 269_696.
while not (((X*X) mod 1_000_000) = 269_696) loop
-- When the computer goes here, the number was not 269_696.
X := X+1;
-- So we replace X by X+1, and then go back and try again.
end loop;
-- When the computer eventually goes here, the number is 269_696.
-- E.e., the value stored at X is the value we are searching for.
-- We still have to print out this value.
Ada.Text_IO.Put_Line(Number'Image(X));
-- Number'Image(X) converts the value stored at X into a string of
-- printable characters (more specifically, of digits).
-- Ada.Text_IO.Put_Line(...) prints this string, for humans to read.
-- I did already run the program, and it did print out 25264.
end Babbage_Problem;