MathDB
m | n^{2016}+n^{2015}+...+n^2+n+1, n |m^{2016}+m^{2015} +...+m^2+m+1

Source: Rioplatense 2017 L3 P3

October 19, 2022
number theorydivides

Problem Statement

Show that there are infinitely many pairs of positive integers (m,n)(m,n), with m<nm<n, such that
mm divides n2016+n2015+⋯+n2+n+1n^{2016}+n^{2015}+\dots+n^2+n+1 and nn divides m2016+m2015+⋯+m2+m+1m^{2016}+m^{2015} +\dots+m^2+m+1.
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