Determine all possible value(s) of a positive integer x such that the base ten number 14....4 is a perfect square, where the digit 4 is repeated precisely x times.

(In reply to re: computer exploration--possible solution (spoiler) by Harry)

Indeed such a search finds no solutions for b < 1000

list
   10   for B=1 to 1000
   20    P=(B*B)@2000
   30    if P=444 then print B
   40   next
OK
run
OK

Posted by Charlie on 2009-08-30 01:49:39