Smallest common difference of arithmetic progressions
Source: Turkey IMO TST 1993 #1
July 7, 2011
modular arithmeticarithmetic sequencenumber theory unsolvednumber theory
Problem Statement
Show that there exists an infinite arithmetic progression of natural numbers such that the first term is and the number of positive divisors of each term is divisible by . Of all such sequences, find the one with the smallest possible common difference.