The solution .x; y/ D .3; 5/ noted by Diophantus is one, and Digby and Wallis
might have agreed it is the only one, since negative numbers had yet to enjoy a fully
equal status with their positive siblings. Presumably the challenge was to show that,
sign apart, there are no others, as Fermat claimed a proof that this solution is unique.
It is not clear from this distance in time if any of the three protagonists ever did have a complete proof of this