‎"LAGRANGE, JOSEPH LOUIS.‎
‎Sur La Solution des Problemes Indéterminés du Second Degré. - [A FUNDAMENTAL PAPER IN THE THEORY OF NUMBERS]‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers as issued in ""Memoires de L'Academie Royale des Sciences et Belles Lettres"", tome XXIII, pp. 165-310.‎

Reference : 32679

‎First edition of a fundamental paper in the Theory of Numbers in which Lagrange gives a solution in integers of indeterminate equations of the second degree - a remarkable turning point in Diophantine analysis. - Fermat had asserted that he could determine when the more general equation x2-Ay2=B was solvable in integers and that he could solve it when solvable, but Lagrange solved it in this paper and furthermore he gives the complete solution to the problem of giving all integral solutions of a general equation where the coefficients are integers. - Cajori calls Lagrange ""One of the greatest mathematicians of all times."" - Poggendorff I:1344.‎