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Let $n$ an even number and $d$ be a divisor of $\frac{n}{2}$. Is there a natural number $1\leq t\leq n$ such that $(n,t)=1$ and $\frac{n}{(n,t-1)}=d$?

$(n,t-1)$ is largest divisor of $n$ and $t-1$.

I think it is true, but can not prove it. Thanks.

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    I think it is true, but can not prove it.2019-03-09

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