A natural number A, when divided by 1981, gave a remainder of 35, and when divided by 1982, it also gave a remainder of 35. What is the remainder when the number $A$ is divided by 14?

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Let $A=1981 k+35=1982 l+35$. Then $1981 k=1982 l$; in particular, $k$ is even. Therefore, the number $1981 k$ is divisible by 14. Hence, when divided by 14, the number A gives the same remainder as 35.

## Answer

7.