7

Part of 2002 JBMO ShortLists

Problems(1)

Prove that at least 3 of the numbers are equal

Source: JBMO Shortlist 2002

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.

algebra proposedalgebra