The Algorithmic Solution of Diophantine Equations

In this book we give some of the local considerations which either allow us to completely solve a diophantine equation, aid us in locating the solutions or give us information about the solutions which can be used in a more advanced method. We show how to apply the p-adic analysis in the Chapter 1 to find solutions to equations using Skolem's method and then finally we discuss how various pieces of local information can be put together in an algorithmic method using sieving. Sieving is no more than a catch-all phrase for a process meaning applying local considerations one after another to sieve out (or remove) non-solutions. The idea behind sieving is that anything left after we have used a sieve has a good chance of being an actual solution.