n(2n + 1)(5n + 2) divides m
Source: Vietnam MO 2008, Problem 3
August 26, 2008
modular arithmeticnumber theoryrelatively primenumber theory unsolved
Problem Statement
Let m \equal{} 2007^{2008}, how many natural numbers n are there such that and n(2n \plus{} 1)(5n \plus{} 2) is divisible by (which means that m \mid n(2n \plus{} 1)(5n \plus{} 2)) ?