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It is conjectured by Erd} os, Graham and Spencer that if 1 a1 a2 as with P s=1 1=ai < n 1=30, then this sum can be decomposed into n parts so that all partial sums are 1. In this note we propose a counterexample which gives a negative answer to this conjecture.

A Counterexample to a Conjecture of Erdős, Graham and Spencer