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Tiling integers

Posted on: April 20th, 2013 by
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A set J of integers is said to tile all integers if there exists a set C such that any integer x can be uniquely written as x=j+c where j is in J and c is in C. Intuitively speaking, J is said to tile integers if integers can be partitioned into disjoint tiles such that each tile is a translate of J.
Show that if J is an infinite set and J tiles integers, then J is periodic (A set J is periodic if there exists a period t such that whenever x is in J, so is x+at for any integer a).

-via ST Aditya
Here is a google search for references.

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