Can anyone give me a hint to solve this problem https://codeforces.me/contest/1152/problem/C please? Thank you
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Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
Соревнования по программированию 2.0
Время на сервере: 23.11.2024 17:26:58 (l1).
Десктопная версия, переключиться на мобильную.
При поддержке
try to make gcd as large as possible; gcd(a,b)=gcd(b-a,a)
let's suppose $$$a \leq b$$$, then $$$\gcd{(a + k, b + k)} = \gcd{(a + k, b - a)}$$$
$$$\gcd{(a + k, b - a)}$$$ is a divisor of $$$b - a$$$
for each $$$d$$$, divisor of $$$b - a$$$, we are trying to find such k that $$$\gcd{(a + k, b - a)} = d$$$
one more hint?
d is a divisor of a + k, so there is a integer n that a + k = n * d. Therefore, k = n * d — a. We also want k to be as small as possible, so n should be as small as possible.