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Omni-MATH / Let m>1 be an integer. Find the smallest positive integer n, such that for any integers a₁,a₂,…,a_(n);b₁,b₂,…,b_(n) there exists integers x₁,x₂,…,x_(n) satisfying the following two…
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problem
Let be an integer. Find the smallest positive integer , such that for any integers there exists integers satisfying the following two conditions:
i) There exists such that and are coprime
ii)
$\sum^n_{i=1} a_ix_i \equiv \sum^n_{i=1} b_ix_i \equiv 0 \pmod m$Plain-text mathematical notation (without MathML)
Let m>1 be an integer. Find the smallest positive integer n, such that for any integers a₁,a₂,…,a_(n);b₁,b₂,…,b_(n) there exists integers x₁,x₂,…,x_(n) satisfying the following two conditions:
i) There exists i∈{1,2,…,n} such that x_(i) and m are coprime
ii) $\sum^n_{i=1} a_ix_i \equiv \sum^n_{i=1} b_ix_i \equiv 0 \pmod m$Original LaTeX notation
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) $\sum^n_{i=1} a_ix_i \equiv \sum^n_{i=1} b_ix_i \equiv 0 \pmod m$Discussion
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