MathDB
1989 | a_n= n^6 +5n^4 -12n^2 -36

Source: Romania IMO TST 1989 1.1

February 17, 2020
Sequencenumber theoryprime

Problem Statement

Let the sequence (ana_n) be defined by an=n6+5n4−12n2−36,n≥2a_n = n^6 +5n^4 -12n^2 -36, n \ge 2. (a) Prove that any prime number divides some term in this sequence. (b) Prove that there is a positive integer not dividing any term in the sequence. (c) Determine the least n≥2n \ge 2 for which 1989∣an1989 | a_n.
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