I have a math problem at school, but i haven't idea how to solve this problem↵
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Given three natural numbers $n, a, b$. We define a pair $(x, y)$ as a *beautiful pair* if it satisfies all the following conditions:↵
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* $1 \leq x \leq a$↵
* $1 \leq y \leq b$↵
* $(x \times y)$ is divisible by $(x + y)$ and the division result does not exceed $n$.↵
* $x$ and $y$ are natural numbers.↵
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**Requirement:** Count the number of pairs $(x, y)$ that satisfy the conditions above and are considered beautiful pairs.↵
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**Input**↵
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* Contains three natural numbers $n, a, b$ $(1 \leq n, a, b \leq 10^{10})$.↵
* The data ensures that the result of the problem will not exceed $10^{18}$.↵
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**Output**↵
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* Print the result after performing the required task.↵
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time limit per test: 2 seconds↵
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can you help me how to solve this problem ↵
↵
(I use a translator to write this post, sorry for my bad English)↵
↵
↵
Given three natural numbers $n, a, b$. We define a pair $(x, y)$ as a *beautiful pair* if it satisfies all the following conditions:↵
↵
* $1 \leq x \leq a$↵
* $1 \leq y \leq b$↵
* $(x \times y)$ is divisible by $(x + y)$ and the division result does not exceed $n$.↵
* $x$ and $y$ are natural numbers.↵
↵
**Requirement:** Count the number of pairs $(x, y)$ that satisfy the conditions above and are considered beautiful pairs.↵
↵
↵
**Input**↵
↵
* Contains three natural numbers $n, a, b$ $(1 \leq n, a, b \leq 10^{10})$.↵
* The data ensures that the result of the problem will not exceed $10^{18}$.↵
↵
↵
**Output**↵
↵
* Print the result after performing the required task.↵
↵
time limit per test: 2 seconds↵
↵
can you help me how to solve this problem ↵
↵
(I use a translator to write this post, sorry for my bad English)↵
↵
