Question 177
Let $n \geqslant 5$ be an integer, and $\{a_{1}, a_{2}, \cdots, a_{n}\}=\{1,2, \cdots, n\}$. Prove that the numbers $a_{1}, a_{1}+a_{2}, a_{1}+a_{2}+a_{3}, \cdots, a_{1}+a_{2}+\cdots+a_{n}$ give at least $\lfloor\sqrt{n}\rfloor+1$ distinct remainders modulo $n$.
($\lfloor.\rfloor$ denotes the integer part.)
($\lfloor.\rfloor$ denotes the integer part.)