On Convergents of Proper Continued Fractions
On Convergents of Proper Continued Fractions
Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their convergents and classify which pairs of integers $p,q$ yield a convergent $p/q$ to some irrational $x$. Notably, we …