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 Minimum Value with RMS (Posted on 2009-12-29)
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.

 No Solution Yet Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 computer solution Comment 2 of 2 |

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   nextOKrun 1       1.0 337     195.0 65521   37829.0 12710881        7338631.0OK`
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 Posted by Charlie on 2009-12-29 14:58:11

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