The digital root of a number is obtained by summing its digits and then repeating the process (summing the sum's digits) until the answer is a single digit number. For example, the digital root of 7368 is 6.

Determine the digital root of (9⁷²⁴⁰+38)⁸⁴⁵⁷

(In reply to Difficulty by Sir Percivale)

I believe that this problems difficulty is derived more from the obsurity of the knowledge requried to solve this problem and not so much from the amount of skill required to solve it once the basic tools are available.  Now concerning the knowledge required,  I simply used google to refresh my memory about digital roots (I remember having a discussion about them in a number theory class back in college many years ago).  One of the first results given by google gave me to the two properties that I used to solve the problem.  So in closing this is more of a challenge of being able to see past the smoke and mirrors of the huge exponents and realize that in modular arithmetic no exponent is too big to work with :-D

Posted by Daniel on 2006-06-29 22:53:04