In his letter to Carcavi (August 1659), Fermat mentions the following challenge
There is no number, one less than a multiple of $3$, composed of a square and the triple of another square.
He says that he has solved it using infinite descent. The next problem that he proposes in the same letter is also solved by him using infinite descent (which was discovered in his copy of Diophantus Arithematica).
However, this question is not particularly clear to me, as to what is being asked to prove here. Can anyone please restate it using modern notations and provide a proof using Infinite Descent?
Thanks in advance.