Toán Olympic quốc tế 2007 Tiếng Anh
... n+1 and f (2007) ≤ 2008. Now we will prove that f (2007) can be any of the numbers 1, 2, . . . , 2008. Define the functions f j (n) = 1, n ≤ 2007 − j, n + j 2007, otherwise. , j ≤ 2007, and f 2008 (n) ... functions f j (n) = 1, n ≤ 2007 − j, n + j 2007, otherwise. , j ≤ 2007, and f 2008 (n) = n, 2007 ∤ n, n + 1, 2007 | n. It is easy to verify that f j satisfy the conditions of...
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