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n^2+n+1-numbers

Source: Nordic Mathematical Contest 2017 Problem 1

April 4, 2017
algebranumber theory

Problem Statement

Let nn be a positive integer. Show that there exist positive integers aa and bb such that a2+a+1b2+b+1=n2+n+1. \frac{a^2 + a + 1}{b^2 + b + 1} = n^2 + n + 1.
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