On a Problem of P . Erdös and S. Stein

نویسنده

  • S. Stein
چکیده

is called a covering system if every integer satisfies at least one of the congruences (1) . An old conjecture of P . Erdös states that for every integer a there is a covering system with n l = c. Selfridge and others settled this question for c < 8 . The general case is still unsettled and seems difficult . A system (1) is called disjoint if every integer satisfies at most one of the congruences (1) . It is trivial that in a disjoint system we must have k (ni, n;) > 1 and Y 1/ni < 1 . i-1

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تاریخ انتشار 1968