IMO 2010 Shortlist C7
Let P1,...,Ps be arithmetic progressions of integers, the following conditions being satisfied: (i) each integer belongs...
Category: Combinatorics
Problem
Let P1,...,Ps be arithmetic progressions of integers, the following conditions being satisfied: (i) each integer belongs to at least one of them; (ii) each progression contains a number which does not belong to other progressions. Denote by n the least common multiple of steps of these progressions; let n pα1 1 ...pαk k be its prime factorization. Prove that s ©1 k ¸ i1 αippi 1q. (Germany)