MathDB

2

Part of 1974 Vietnam National Olympiad

Problems(1)

(a) 9/n, 25/ (n+1), (b)12/n, 165/(n+1) , (c) 9/n, 25/(n+1), 4/(n+2)

Source: Vietnamese MO (VMO) 1974

8/20/2018
i) How many integers nn are there such that nn is divisible by 99 and n+1n+1 is divisible by 2525? ii) How many integers nn are there such that nn is divisible by 2121 and n+1n+1 is divisible by 165165? iii) How many integers nn are there such that nn is divisible by 9,n+19, n + 1 is divisible by 2525, and n+2n + 2 is divisible by 44?
number theoryDivisibility