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).

Charlie, suppose that DJ did not note that the square roots of the given sequence of numbers are of the form 7, 67, 667, 6667, ....etc. then how would you proceed to prove the numbers of the given form to be perfect squares ?

Posted by Ravi Raja on 2003-04-06 04:12:57