On a conjecture of R. L. Graham
نویسندگان
چکیده
منابع مشابه
On a conjecture of Butler and Graham
In this paper we prove a conjecture of Bulter and Graham [2] on the existence of a certain way of marking the lines in [k] for any prime k. The conjecture states that there exists a way of marking each line of [k] one point so that every point in [k] is marked exactly a or b times as long as the parameters (a, b, n, k) satisfy the condition that there are integers s, t such that s + t = k and a...
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It is conjectured by Erdős, Graham and Spencer that if 1 ≤ a1 ≤ a2 ≤ · · · ≤ as are integers with ∑s i=1 1/ai < n − 1/30, then this sum can be decomposed into n parts so that all partial sums are ≤ 1. This is not true for ∑s i=1 1/ai = n − 1/30 as shown by a1 = · · · = an−2 = 1, an−1 = 2, an = an+1 = 3, an+2 = · · · = an+5 = 5. In 1997 Sandor proved that Erdős–Graham–Spencer conjecture is true ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1996
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-75-1-1-38