# Small solutions to linear coprime Diophantine equations

Suppose I have integers $$a_1, …, a_n$$ which are coprime, meaning that

$$a_1 b_1 + … + a_n b_n = 1$$

has a solution in integers $$b_1, …, b_n$$. I would like to get a bound saying something like

There exists a solution with $$\sum_i |b_i| < \sum_i |a_i|$$ (except in the degenerate case where $$a_j = 1$$, $$a_i = 0$$ for $$i \neq j$$)

Presumably such things (and probably much stronger bounds) are known. Does anyone know a reference for these kinds of results?