

Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:

 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.



Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.

For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].



Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.




; The computer will evaluate expressions written in -- possibly nested -- parentheses, where the first symbol gives the operation and any subsequent symbols or numbers give the operands.
 
; For instance, (+ (+ 2 2) (- 7 5)) evaluates to 6.
 
; We define our problem as a function:
 
(define (try n)
 
; We are looking for a value of n that leaves 269,696 as the remainder when its square is divided by a million.
 
; The symbol * stands for multiplication.
 
    (if (= (remainder (* n n) 1000000) 269696)
 
; If this condition is met, the function should give us the value of n:
 
        n
 
; If not, it should try n+1:
 
        (try (+ n 1))))
 
; We supply our function with 1 as an initial value to test, and ask the computer to print the final result.
 
(print (try 1))