On a problem of P. Erdos and S. Stein
نویسندگان
چکیده
منابع مشابه
On a Problem of P . Erdös and S. Stein
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 congruenc...
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Let a 1 < a2 < • , • be an infinite sequence of integers satisfying an = (c + o(l))na for some a > 1 . One can ask: Is it likely that ati + aj = ar or, more generally, ai, + • • • + ai ,, = ai , has infinitely many solutions. We will formulate this problem precisely and show that if a > 3 then with probability 1, ai + aj = a r has only finitely many solutions, but for a :-!5 3, ai + aj = ar has...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1968
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-15-1-85-90