Sequences related to convergents to square root of rationals

نویسنده

Mario Catalani

چکیده

1 The Initial Results This note has its source in [3], in a different setting. Consider the system of recurrences, with a 0 = b 0 = 1, a n = a n−1 + kb n−1 , (1) b n = a n−1 + b n−1. (2) Later on we will generalize and show that the ratio an bn is related to conver-gents to the square root of rationals. We postpone the proof by induction of the following formulas (" summation formulas ")

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