1000 digits 500 products
Source: CentroAmerican & Caribbean MO 1999 Q2
January 24, 2007
modular arithmeticnumber theory proposednumber theory
Problem Statement
Find a positive integer with 1000 digits, all distinct from zero, with the following property: it's possible to group the digits of into 500 pairs in such a way that if the two digits of each pair are multiplied and then add the 500 products, it results a number that is a divisor of .