All Questions

Suppose I have integers $a_1, \dots, a_n$ which are coprime, meaning that $$a_1 b_1 + \dots + a_n b_n = 1$$ has a solution in integers $b_1, \dots, b_n$. I would like to get a bound saying ...

Let $n$ be positive integer, $k$,$B$ fixed positive integers. Let $f_i(x_1,x_2...x_n)$ be a system of $n-k$ linearly independent linear equations over the integers. Let $S(f_i,k,B)$ be the set of ...