MathDB
(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

August 20, 2018
number theoryDivisibility

Problem Statement

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?
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