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It is conjectured by Erd˝ os, Graham and Spencer that if 1 ≤ a 1 ≤ a 2 ≤ · · · ≤ a s are integers with s i=1 1/a i < 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/a i = n − 1/30 as shown by a 1 = · · · = a n−2 = 1, a n−1 = 2, a n = a n+1 = 3, a n+2 = · · · = a n+5 = 5. In 1997 Sandor… (More)

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