2003 IMO Problems/Problem 1

is the set $\set{1, 2, 3, . . . , 1000000}$ (Error compiling LaTeX. Unknown error_msg). Show that for any subset of with elements we can find distinct elements of , such that the sets $\set{a + x_i \mid a \in A}$ (Error compiling LaTeX. Unknown error_msg) are all pairwise disjoint.