Determine the minimum value of P for which the root mean square (RMS) of the first P positive integers (that is; 1, 2,..., P) is an integer, where P is a positive integer > 1.

The answer is 337, based on ignoring the value of 1 in the list of the first four solutions:

        P             RMS
        1              1.0
      337            195.0
    65521          37829.0
 12710881        7338631.0

list
   10   for P=1 to 99999999
   20   Tot=Tot+P*P
   30   Avg=Tot//P
   40   Rms=sqrt(Avg)
   50   Irms=int(Rms+0.5)
   60   if Irms*Irms=Avg then print P,Rms
   70   next
OK
run
 1       1.0
 337     195.0
 65521   37829.0
 12710881        7338631.0
OK

Posted by Charlie on 2009-12-29 14:58:11