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NO-ABEL 1996 Problem 4

    Let f:N→Nf : N \to N be a function such that f(f(1995))=95,f(xy)=f(x)f(y)f(f(1995)) = 95, f(xy) = f(x)f(y) and f(x)≤xf(x) \le x for all x,yx,y . Find all possible values of f(1995)f(1995) .

    Dataset text AI-MO AoPS. Quoted with source.

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