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N_0 is the union of all disjoint olympic sets

Source: India tst 2002 p12

July 13, 2012

algorithminvariantgeometrygeometric transformationalgebrapolynomialcombinatorics unsolved

Problem Statement

Let

a,b

be integers with

0<a<b

. A set

\{x,y,z\}

of non-negative integers is olympic if

x<y<z

and if

\{z-y,y-x\}=\{a,b\}

. Show that the set of all non-negative integers is the union of pairwise disjoint olympic sets.