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 an algorithm to solve these in the general case – a task we now know to be impossible).
One diophantine set is the integers – which are a solution to
and so on…
- Hilbert’s 10.5th Problem (rjlipton.wordpress.com)
- On the number of solutions to 4/p = 1/n_1 + 1/n_2 + 1/n_3 (terrytao.wordpress.com)
- The Omega Man (beatsnpeace.wordpress.com)
- Counting the number of solutions to the Erdös-Straus equation on unit fractions (terrytao.wordpress.com)
- Hilbert’s seventh problem, and powers of 2 and 3 (terrytao.wordpress.com)