| Problems 73#1.2 Back | |
Hints and comments | |
| Comment: In the original problem the disjointness condition was missing.
Bengt Ek pointed out the following counterexample:
the arithhmetic progressions {2n} , {3n + 1} , {4n + 1} , {6n + 3} , and {12 n + 11} , as n runs through all integer values, exhausts the integers. To see this note that if x belongs to any of these progressions so does x + 12 since the moduli 2, 3, 4, 6, and 12 all divide 12. Therefore the assertion need only be checked for x in the set {1,2,3, ..., 12} , which is straightforward. |
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| Hint 1 | |