# Tag: Diophantine equation

• ## The Erdős–Straus conjecture

I came across this as a result of links to stories about Hilbert’s tenth problem, and it looks fun, so I thought I’d write a little about it. The Erdős–Straus conjecture is that for any integer then where , , and are positive integers. This is equivalent to a diophantine equation: Which is, apparently, trivially…

• ## More on Hilbert’s tenth problem

One of the best things about WordPress.com is that it gives me, as a blog author, the opportunity to link in other relevant stories and so it was with my last post on diaphantine sets and the integers. The top linked item there gives a lot more on David Hilbert‘s “tenth problem” – which was…

• ## Diophantine sets and the integers

This is not some great revelation, but it interested me, so might interest some readers (I got it from The Honors Class: Hilbert’s Problems and Their Solvers). A diophantine equation is one of the form and a diophantine set is a set of numbers to solve a diophantine equation (Hilbert’s 10th problem was to find…