1,1

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 gcd of these moduli. We consider minimal N's, i.e. N is a gcd of some moduli, but none of the divisors has this property.

Donald Jason Gibson, A covering system with least modulus 25, Math. Comp. 78, (2009), 1127-1146.

Pace P. Nielsen, A covering system whose smallest modulus is 40, Journal of Number Theory 129, (2009), 640-666.

Pace P. Nielsen, A movie explaning covering systems.

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 gcd 80. None of the divisors has that property.

36 is not minimal since 12 is a divisor and 12 is the gcd of a covering system.

Cf. A160560.

Sequence in context: A030116 A035042 A061593 this_sequence A038734 A058962 A009500

Adjacent sequences: A160556 A160557 A160558 this_sequence A160560 A160561 A160562

nonn

Matthijs Coster (sequences(AT)matcos.nl), May 19 2009