# Ramanujan might take a little longer on this one

This problem is a much more difficult computer-science follow-up to this question. If you have already read the paragraph about Ramanujan there, you can skip it here.

Today, Sunday, December $22$, is Srinivasa Ramanujan's $126\text{th}$ birthday. Ramanujan was an amazing mathematician, but one of the things he was most famous for had to do with the number $1729$. When Ramanujan was in the hospital, he was visited by his friend G.H. Hardy. Hardy remarked that the taxicab that he had ridden in had a rather uninteresting number: $1729$. Ramanujan said that no, $1729$ was very interesting because it was the smallest number that can be expressed as the sum of $2$ cubes in $2$ different ways. These are $12^3+1^3$ and $10^3+9^3$. Hence, numbers that can be written as the sum of multiple cubes in more than $1$ way are called taxicab numbers. Some more really interesting information about taxicab numbers can be found in this video.

So here's the problem.

Let $f(n)$ be a function that finds the sum of the digits of $n$. What are the last $3$ digits of this expression? $\sum_{i=1}^{17}\sum_{j=1}^{29} f(i^3+j^3)$

×

Problem Loading...

Note Loading...

Set Loading...