12

Part of 2002 India IMO Training Camp

Problems(1)

N_0 is the union of all disjoint olympic sets

Source: India tst 2002 p12

a,b

be integers with

0<a<b

\{x,y,z\}

of non-negative integers is olympic if

x<y<z

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

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

algorithminvariantgeometrygeometric transformationalgebrapolynomialcombinatorics unsolved