English Title
On the resolution of irrationals by continued fractions, where a certain minor new and singular type is set forth
Enestrom Number
454
Fuss Index
93
Original Language
Latin
Content Summary
This paper begins with a review of Pell’s equation and continued fractions. It includes the following problems: (1) Given that the formula Ax2–2Bxy+Cy2 produces the value c when x=a and y=b, find an infinity of other values for x and y that produce that same value c, assuming that the quantity B2–AC is a positive non-square number; (2) Given a formula Ax2–Bxy+Cy2 in which B2–AC is a positive non-square number, find values for x and y that produce the minimum value in this formula.
Topics
Number Theory
Published as
Journal article
Published Date
1774
Written Date
1772
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 18, pp. 218-244.
Opera Omnia Citation
Series 1, Volume 3, pp.310-334.
Record Created
2018-09-25
