IOM 2019, Блиц — Задача 65

OLYMPIAD OF METROPOLISES, Moscow, September 2, 2019 · 2 септември 2019 г.

Условие

There are two integers $x$ and $y$, such that the sum of these two numbers is 105. Then $gcd(x,y)$ and $lcm(x,y)$ of these two numbers are 15 and 150 respectively. What is the difference between the two numbers?

Note: $gcd(x,y)$ is the greatest common divisor of $x$ and $y$, and $lcm(x,y)$ is the least common multiple of $x$ and $y$.

Решение

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Оригинал в Архива: blitz-en-all-task-final.pdf