2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5

Problem

$5^n$ is written on the blackboard. The sum of its digits is calculated. Then the sum of the digits of the result is calculated and so on until we have a single digit. If $n = 2014$, what is this digit?

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it. What you have to realize is that the sum of the digits of a number is the number $\pmod{9}$. We can prove this right now. \begin{equation} \end{equation}

See also

2014 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions
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