MathDB

Let

m>1

be an integer. Find the smallest positive integer

n

, such that for any integers

a_1,a_2,\ldots ,a_n; b_1,b_2,\ldots ,b_n

there exists integers

x_1,x_2,\ldots ,x_n

satisfying the following two conditions:
i) There exists

i\in \{1,2,\ldots ,n\}

such that

x_i

and

m

are coprime
ii)

\sum^n_{i=1} a_ix_i \equiv \sum^n_{i=1} b_ix_i \equiv 0 \pmod m

2