The sum of the base ten logarithms of the divisors of 10^M is 792, where M is a positive integer.

What is the value of M?

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