number theory 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. Reference
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