Problem 3

For any positive integer $n$, let $\sigma(n)$ denote the sum of the digits of $n$, for example, $\sigma(317)=11$. Find the least number $n$ such that $20$ divides $\sigma(n)$ and $26$ divides $\sigma(n+1)$.

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is six plus four, plus nine?

This problem was first solved on Wed 4th February at 4:06:51pm