1978 IMO 第 5 题

(GDR 2) For every integer $d \geq 1$, let $M_{d}$ be the set of all positive integers that cannot be written as a sum of an arithmetic progression with difference $d$, having at least two terms and consisting of positive integers. Let $A=M_{1}, B=M_{2} \backslash\{2\}, C=M_{3}$. Prove that every $c \in C$ may be written in a unique way as $c=a b$ with $a \in A, b \in B$.

(GDR 2) 对于每个整数 $d \geq 1$，令 $M_{d}$ 为所有正整数的集合，这些正整数不能写成差值 $d$ 的算术级数之和，至少有两项且由正整数组成。令 $A=M_{1}, B=M_{2} \反斜杠\{2\}, C=M_{3}$。证明每个$c \in C$ 都可以用唯一的方式写为$c=a b$ 其中$a \in A, b \in B$。