Number leaving remainder n-1 on division by each n

Find the smallest positive integer $x$ such that dividing $x$ by $n$ leaves remainder $n-1$ for every $n=2,3,\dots,10$.

2519. The conditions say $x\equiv-1 \pmod n$ for each $n$, i.e. $x+1$ is a multiple of every number from $2$ to $10$. The least such multiple is $\operatorname{lcm}(2,\dots,10)=2520$, so $x=2519$.