Romania District Olympiad 2001 - VII Grade
Source:
March 12, 2011
modular arithmeticnumber theory proposednumber theory
Problem Statement
A positive integer is called good if it can be written as a sum of two consecutive positive integers and as a sum of three consecutive positive integers. Prove that:a)2001 is good, but 3001 isn't good.
b)the product of two good numbers is a good number.
c)if the product of two numbers is good, then at least one of the numbers is good.Bogdan Enescu