Number theory is the study of the whole numbers and their properties and relationships. Often, a problem in number theory can be restated in terms of finding the solution, or showing that there is no solution, to a Diophantine equation. A Diophantine equation is one where the coefficients are whole numbers, and where the solution is also constrained to be a whole number. Sometimes, what appears to be a simple Diophantine equation can lead to an elliptic curve.
1. Beiler, Albert H. Recreations in the Theory of Numbers. Mineola, NY: Dover, 1964.