IMO Shortlist 1996 problem N3

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Dodao/la: arhiva
2. travnja 2012.
A finite sequence of integers a_0, a_1, \ldots, a_n is called quadratic if for each i in the set \{1,2 \ldots, n\} we have the equality |a_i - a_{i-1}| = i^2.

a.) Prove that any two integers b and c, there exists a natural number n and a quadratic sequence with a_0 = b and a_n = c.

b.) Find the smallest natural number n for which there exists a quadratic sequence with a_0 = 0 and a_n = 1996.
Izvor: Međunarodna matematička olimpijada, shortlist 1996