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A160559
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Minimal covering numbers.
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2
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12, 80, 90, 210, 280, 378, 448, 1650, 2200, 2464, 5346, 9750, 11264, 13000, 14994, 15246, 18018, 18954, 20384, 23166, 23562, 26334, 26656, 27846, 30294, 31122, 31878, 33150, 33858, 36608, 37050, 37674, 40194, 42966, 44200, 44850, 49400, 49504, 51282, 53248, 53900, 55328, 56826, 59598, 59800, 63750, 65142, 66976, 67914, 71250, 72930, 73458
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OFFSET
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1,1
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COMMENTS
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A collection of congruences with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a covering system. Let N be the LCM of these moduli. We consider minimal N's, i.e., N is the LCM of some moduli, but none of the divisors has this property.
Hough and Nielsen (2019) proved that each term must be divisible by 2 or 3. - Max Alekseyev, Nov 19 2022
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LINKS
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EXAMPLE
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80 is in the set since 1 mod 2; 2 mod 4; 4 mod 8; 8 mod 16; 4 mod 5; 8 mod 10; 16 mod 20, 32 mod 40; 0 mod 80 is a covering system with LCM 80. None of the divisors has that property.
36 is not minimal since 12 is a divisor and 12 is the LCM of a covering system.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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