Approximating reals by sums of two rationals Original Research Article

We generalize Dirichletʹs diophantine approximation theorem to approximating any real number α by a sum of two rational numbers image with denominators 1less-than-or-equals, slantq1,q2less-than-or-equals, slantN. This turns out to be related to the congruence equation problem image with 1less-than-or-equals, slantx,yless-than-or-equals, slantq1/2+epsilon (Porson).