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All sums a_i + a_j are distinct

Source: French TST 2002

June 17, 2011
number theory proposednumber theory

Problem Statement

Let p≥3p\ge 3 be a prime number. Show that there exist pp positive integers a1,a2,…,apa_1,a_2,\ldots ,a_p not exceeding 2p22p^2 such that the p(p−1)2\frac{p(p-1)}{2} sums ai+aj (i<j)a_i+a_j\ (i<j) are all distinct.
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