Prove that at least 3 of the numbers are equal
Source: JBMO Shortlist 2002
November 12, 2008
algebra proposedalgebra
Problem Statement
Consider integers a_i,i\equal{}\overline{1,2002} such that
a_1^{ \minus{} 3} \plus{} a_2^{ \minus{} 3} \plus{} \ldots \plus{} a_{2002}^{ \minus{} 3} \equal{} \frac {1}{2}
Prove that at least 3 of the numbers are equal.