Diophantine Equation y cubed equals x squared plus 2/Historical Note

Historical Note on Diophantine Equation $y^3 = x^2 + 2$
The Diophantine equation $y^3 = x^2 + 2$ was proved to have only the solution $x = 5, y = 3$ by by use of the Method of Infinite Descent.

He submitted it, without proof, along with a number of others, to in a letter dated $14$ August $1659$.