algorithmic number theory msripublications volume44 2008 solving the pell equation hendrik w lenstra jr abstract weillustrate recent developments in computational number the ory by studying their implications for solving the ...
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...Algorithmic number theory msripublications volume solving the pell equation hendrik w lenstra jr abstract weillustrate recent developments in computational ory by studying their implications for we shall see that if solutions to are properly represented tradi tional continued fraction method can be signicantly accelerated most promising depends on use of smooth num bers as with manyalgorithmsdependingonsmoothnumbers itsruntimecan presently only conjecturally established giving a rigorous analysis is one many open problems surrounding s x ddyc solved positive integers y given nonzero integer d example take always assume but not square since otherwise there clearly no theenglishmathematicianjohnpell hasnothingtodowiththe euler mistakenlyattributedtopellasolutionmethodthat had fact been found another english mathematician william brouncker response challenge fermat attempts change terminology introduced have proved futile has an extraordinarily rich history which weil best guide also subs...