Approximating reals by sums of two rationals
Tsz Ho Chan
Abstract
We generalize Dirichlet's diophantine approximation theorem to approximating any real number α by a sum of two rational numbers a1q1 + a2q2 with denominators 1 ≤ q1, q2 ≤ N. This turns out to be related to the congruence equation problem x y c q with 1 ≤ x, y ≤ q1/2 + ε.
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