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Quadratic permutations

Source: Moldova IMO-BMO TST 2003, day 3, problem 1.

August 16, 2008
quadraticsnumber theoryrelatively primeDiophantine equation

Problem Statement

Let n∈N∗ n\in N^*. A permutation (a1,a2,...,an) (a_1,a_2,...,a_n) of the numbers (1,2,...,n) (1,2,...,n) is called quadratic iff at least one of the numbers a_1,a_1\plus{}a_2,...,a_1\plus{}a_2\plus{}a\plus{}...\plus{}a_n is a perfect square. Find the greatest natural number n≤2003 n\leq 2003, such that every permutation of (1,2,...,n) (1,2,...,n) is quadratic.
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