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# Tag Archives: sum

## A new tricubic sum for three!

Here’s a nice Numberphile interview with Andrew Booker about the new discovery. They also talk about Hilbert’s tenth problem, undecidability, the reasons for doing computer searches like this, the role of science communication (such as Numberphile) in spurring discovery, and … Continue reading

Posted in number theory
Tagged cubes, multiple, number theory, representation, sum

## Sums of cubes: multiple representations

I’m continuing a short series of posts on representing numbers as a sum of three cubes; previous posts are 33 is the sum of three cubes and More sums of three cubes. We now know that every number less than … Continue reading

## More sums of three cubes

About six months ago I wrote about the recent discovery that 33 can be written as the sum of three cubes. At that time, the only remaining number less than 100 whose status was still unknown was 42. And just … Continue reading

## 33 is the sum of three cubes

I’m a bit late to the party, but I find this fascinating: we now know (thanks to a discovery of Andrew R. Booker) that the number 33 can be written as the sum of three cubes. This may sound unremarkable, … Continue reading

Posted in number theory
Tagged cubes, number theory, sum

## Iterating squared digit sums in other bases

In a previous post I wrote about iterating the squared digit sum function, which adds up the sum of the squares of the digits of a number; for example, . Denis left a comment asking about other bases—what happens if … Continue reading

## Iterating squared digit sum

Another fun fact I learned from John Cook. Let be the function which takes a positive integer and outputs the sum of the squares of its digits. For example, . Since the output is itself another positive integer, we can … Continue reading

Posted in arithmetic, computation, proof
Tagged digit, loop, Porges, proof, squared, sum
12 Comments

## More on sums of palindromes

In my previous post I reported on a recent proof that every positive integer can be written as the sum of three palindromes. The first thing to report in this follow-up post is that Lewis Baxter sent me the Python … Continue reading