The word Diophantine refers to Diophantus, the third century mathematician from Alexandria. Numbers are the fundamental building blocks of mathematics, so he started thinking about problems for which we need integer solutions. For example, how many horses do we need to achieve a particular task? Even if the exact answer is 15.5, we cannot really cut the last horse into half. So he started studying these problems in order to develop a sound framework around it. This went on to become one of the most enigmatic and endearing fields in the history of mathematics. Diophantine equations have become so fundamental that we cannot imagine our world without them. Let’s go ahead and see what they are all about, shall we?   Continue reading “Dissecting Diophantine Equations” →