Tag Archives: sum

A new tricubic sum for three!

Posted on September 24, 2019 by Brent

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 →

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Sums of cubes: multiple representations

Posted on September 16, 2019 by Brent

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 →

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More sums of three cubes

Posted on September 13, 2019 by Brent

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 →

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33 is the sum of three cubes

Posted on March 30, 2019 by Brent

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 →

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Iterating squared digit sums in other bases

Posted on May 25, 2018 by Brent

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 →

Posted in arithmetic, computation, proof | Tagged , , , , | 7 Comments

Iterating squared digit sum

Posted on April 26, 2018 by Brent

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 , , , , , | 12 Comments

More on sums of palindromes

Posted on April 11, 2018 by Brent

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 →

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Every positive integer is a sum of three palindromes

Posted on April 9, 2018 by Brent

I recently learned from John Cook about a new paper by Javier Cilleruelo, Florian Luca, and Lewis Baxter proving that every positive integer can be written as a sum of three palindromes. A palindrome is a number that is the … Continue reading →

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The MacLaurin series for sin(x)

Posted on February 13, 2017 by Brent

In my previous post I said “recall the MacLaurin series for :” Since someone asked in a comment, I thought it was worth mentioning where this comes from. It would typically be covered in a second-semester calculus class, but it’s … Continue reading →

Posted in calculus, infinity, iteration | Tagged , , , , , , , | 4 Comments

The Basel problem

Posted on February 6, 2017 by Brent

I wanted to follow up on something I mentioned in my previous post: I claimed that At the time I didn’t know how to prove this, but I did some quick research and today I’m going to explain it! It … Continue reading →

Posted in infinity, number theory | Tagged , , , , , | 9 Comments