x^n + (2+x)^n + (2-x)^n = 0
Source: IMO LongList 1988, Hong Kong 4, Problem 28 of ILL
October 22, 2005
calculusintegrationmodular arithmeticalgebrapolynomialalgebra unsolved
Problem Statement
Find a necessary and sufficient condition on the natural number for the equation
x^n \plus{} (2 \plus{} x)^n \plus{} (2 \minus{} x)^n \equal{} 0
to have a integral root.