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math.NT2003
Sequences related to convergents to square root of rationals
Mario Catalani
In this note we study some sequences whose ratio converges to the square root of rationals. Further we analyze some related sequences obtained when the above mentioned ratio simpli…
math.CO2003
Sequences related to the Pell generalized equation
Mario Catalani
We consider sequences of the type ( and integers) and show that all sequences that solve particular cases of the Pell generalized equati…
math.NT2003
On the average of triangular numbers
Mario Catalani
The problem we are dealing with is the following: find two sequences and such that the average of the first triangular numbers (starting with the triangular numbe…