euler and lagrange on pell s equation joshua aaron mcgill id 260352168 december 3 2010 introduction the eld of number theory is notorious for yielding immensely dicult problems that are ...
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...Euler and lagrange on pell s equation joshua aaron mcgill id december introduction the eld of number theory is notorious for yielding immensely dicult problems that are deceptively easy to state one such problem known as was studied by some greatest mathematicians th in history not fully solved until century here we will show early attempts at solving this indian mathematician brahmagupta ce who forged an identity still used modern mathematics bhaskara ii develope chakravala method which he then ecient means computing solutions nearly years later leonard gave depth analysis other diophantine equations his book elements algebra leaned earlier wallis ways reminiscent cyclic presented dierence lies fact far more rigorous description principle induction a precursor innite descent whereas simply stated results never told how discovered ingenious six after published thirty ve year old joseph made signicant additions volume entitled well providing corrections comments includes proof reducibil...