Bachet, in his famous 1621 Latin translation of the Arithmetica of Diophantus,
noted that from the one solution 52 C 2 D 33 other rational numbers r may be found
with the property that r 2 C 2 is a cube of a rational number. Fermat acquired a copy
of this work, and by 1636 had studied it carefully and made significant advances. He
also recorded several of his most influential marginal notes in this book, including the
comment concerning Fermat’s last theorem