Concerning the use of a new algorithm to solve the Pell problem
According to Academy records, this work was presented to the St. Petersburg Academy twice: first on October 15, 1759, and again on May 23, 1763.
This is where Euler calls it Pell's equation and uses continued fractions to solve it.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 11, pp. 28-66.
Opera Omnia Citation
Series 1, Volume 3, pp.73-111.