444444....4444888888....8889

[Where there are 'k' Fours, '(k-1)' Eights and 'Exactly One' 9],

are always perfect squares.

(For example the sequence of numbers: 49, 4489, 444889, ....etc. and so on are always perfect squares).

This method Charlie, that you have used to prove the result is actually back-calculation or manipulation what I would say, since you came to know the form in which the square roots of the numbers in the sequence are.

Posted by Ravi Raja on 2003-04-06 04:18:56