Abstract
We generalize Dirichlet's diophantine approximation theorem to approximating any real number α by a sum of two rational numbers a 1 q 1 + a 2 q 2 with denominators 1 ⩽ q 1 , q 2 ⩽ N . This turns out to be related to the congruence equation problem x y ≡ c ( mod q ) with 1 ⩽ x , y ⩽ q 1 / 2 + ϵ .
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