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.

Considering all x up to 2300, only x=2 and x=3, corresponding to 144 = 12^2 and 1444 = 38^2, work:

list
   10   N=14
   20   for X=1 to 2300
   30    Sr=int(sqrt(N)+0.5)
   40    if Sr*Sr=N then print X,Sr
   50    N=N*10+4
   60   next
OK
run
 2       12
 3       38
OK

Posted by Charlie on 2009-08-29 19:24:11