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$a^n+b^n+c^n$

Source: Austrian MO 2005 round 1

June 27, 2005

algebra unsolvedalgebra

Problem Statement

For 3 real numbers

a,b,c

let

s_n=a^{n}+b^{n}+c^{n}

. It is known that

s_1=2

s_2=6

and

s_3=14

. Prove that for all natural numbers

n>1

, we have

|s^2_n-s_{n-1}s_{n+1}|=8