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.
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.