The integers are one of the most studied areas of mathematics and yet we keep keep learning new things about them. Today comes this bit of knowledge: Any positive integer can be written as the sum of three palindromes. More precisely, this is based on a paper Every Positive Integer Is A Sum Of Three Palindromes by Javier Cilleruelo, Florian Luca, and Lewis Baxter that makes the claim that “For integer g ≥ 5, we prove that any positive integer can be written as a sum of three palindromes in base g.”

Here is an interactive site based on this result. It invites you to write down any number, however large, and then watch as it is given as the sum of three palindromic numbers. Go on, try it!

Numbers are fascinating things. it is not surprising that number theory attracts some of the finest mathematicians.