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A160560
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Almost minimal covering numbers
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1
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2, 4, 6, 8, 16, 18, 30, 32, 40, 54, 64, 126, 128, 150, 162, 200, 224, 256, 486, 512, 750, 882, 1000, 1024, 1458, 1568, 1782, 1950, 2048, 2600, 2912, 3750, 4096, 4374, 5000, 5632
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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. If modulo N one number is uncovered then we speak about an almost minimal covering number.
We denote by T(N) the number of divisors of N. We denote by R(N) the number of uncovered numbers modulo N. Suppose N=p^k.M, where gcd(p,M)=1, p prime, R(M) = 1 and T(M) = p-1 then R(N) = 1 as well. R(p) = p-1.
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LINKS
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EXAMPLE
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30 is an almost minimal covering number since 1 mod 2; 2 mod 3; 4 mod 5; 4 mod 6; 8 mod 10; 12 mod 15 and 6 mod 30 covers all numbers modulo 30 except 30-folds.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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