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Log Divisor Sum (Posted on 2014-08-01) Difficulty: 3 of 5
The sum of the base ten logarithms of the divisors of 10M is 792, where M is a positive integer.

What is the value of M?

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

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Solution anal. solution Comment 2 of 2 |

For odd values of M the divisors can be grouped in couples such that

sum of logs in each couple will be M:

1,10^M;  2, 10^M/2;....d, 10^M/d.

Clearly there are .5*(M+1)^2  couples, so

.5*(M+1)^2*M=792

and  M=11

For even  values of M the formula is slightly different, but it is immaterial now.

Edited on August 1, 2014, 3:09 pm
  Posted by Ady TZIDON on 2014-08-01 13:54:00

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