Let n be the element of N and let a1,a2,...,an be positive real numbers such that

a1+a2+a3+...+an= (1/(a1)^2)+(1/(a2)^2)+...+(1/(an)^2)

Prove that for any m=1,2,...,n there exist m numbers among ai whose sum is at least m.

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- Apr 11th 2011, 07:11 PMchris86Prove that exists m among ai whose sum is at least m
Let n be the element of N and let a1,a2,...,an be positive real numbers such that

a1+a2+a3+...+an= (1/(a1)^2)+(1/(a2)^2)+...+(1/(an)^2)

Prove that for any m=1,2,...,n there exist m numbers among ai whose sum is at least m.