IMO Shortlist 1990 problem 7


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2. travnja 2012.
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Let f(0) = f(1) = 0 and

f(n+2) = 4^{n+2} \cdot  f(n+1) - 16^{n+1} \cdot f(n) + n \cdot 2^{n^2}, \quad n = 0, 1, 2, \ldots

Show that the numbers f(1989), f(1990), f(1991) are divisible by 13.
Izvor: Međunarodna matematička olimpijada, shortlist 1990