MathDB

3

Part of 2017 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

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

Source: Rioplatense 2017 L3 P3

10/19/2022
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.
number theorydivides