On the solvability of the equation ∑ⁿᵢ₌₁𝑥ᵢ/𝑑ᵢ≡0(𝑚𝑜𝑑1) and its application
On the solvability of the equation ∑ⁿᵢ₌₁𝑥ᵢ/𝑑ᵢ≡0(𝑚𝑜𝑑1) and its application
In this paper, we obtain a necessary and sufficient condition under which the equation of the title is unsolvable. More precisely, for the equation <disp-formula content-type="math/mathml"> \[ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction x 1 Over d 1 EndFraction plus StartFraction x 2 Over d 2 EndFraction plus midline-horizontal-ellipsis plus StartFraction x Subscript …