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n^6 + 5n^3 + 4n + 116 is the product of two or more consecutive numbers

Source: Bulgaria JBMO TST 2018, Day 1, Problem 3

June 25, 2018
number theoryDiophantine equation

Problem Statement

Find all positive integers nn such that the number n6+5n3+4n+116n^6 + 5n^3 + 4n + 116 is the product of two or more consecutive numbers.
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