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I want to prove the following:

Let $m_0,...m_r$ be pairwise coprime integers . Show that there exists a sequence of consecutive integers $s, s+1,...,s+r$ such that $m_i\vert s+i, i =0,...,r$

I know that consecutive number are coprime and then $gcd(s_j,s_{j+1}) =1$ . Because the mi's are pairwise coprime I thought about the Chinese Remainder Theorem but I don't think it's the right way

Any hint on how to proceed ?

Physmath
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  • Solve for $x$ the following equivalence relations: $x\equiv -i\pmod {m_i}$ for $0\le i\le r$ –  Oct 04 '18 at 18:54

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