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# Tag Archives: algorithm

## 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

## Every positive integer is a sum of three palindromes

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

Posted in arithmetic, computation, links
Tagged algorithm, constructive, news, palindromes, proof, sum
14 Comments

## Fast and slow machines

In my previous post, I presented three hypothetical machines which take a positive integer as input and give us something else as output: a factorization machine gives us the complete prime factorization of ; a factor machine gives us one … Continue reading

Posted in computation, number theory, primes
Tagged algorithm, division, efficiency, exponential, factor, factorization, machine, polynomial, primality, testing, trial
1 Comment

## From primitive roots to Euclid’s orchard

Commenter Snowball pointed out the similarity between Euclid’s Orchard… …and this picture of primitive roots I made a year ago: At first I didn’t see the connection, but Snowball was absolutely right. Once I understood it, I made this little … Continue reading

## A few words about PWW #20

A couple commenters quickly figured out what my previous post without words was about. The dots making up the image are at integer grid points , with the center at . There is a dot at if and only if … Continue reading