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min integer in form (n^a-n^b)/ (n^c-n^d)

Source: 2006 VMEO III Shortlist SL N12 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__viet

October 28, 2021
number theoryInteger

Problem Statement

Given a positive integer n>1n > 1. Find the smallest integer of the form na−nbnc−nd\frac{n^a-n^b}{n^c-n^d} for all positive integers a,b,c,da,b,c,d.
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