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Let $S_m=a^m+b^m+c^m,p=ab+bc+ca$ and $q=abc$

$$S_{m+3}=3S_{m+2}-pS_{m+1}+qS_m$$

Suppose $S_1=3, S_2=5, S_3=12$. I am wondering how to use strong induction, if possible, to prove the above statement?

user82479
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    Is this related to this question? https://math.stackexchange.com/questions/2891979/solving-complex-number-equation-with-galois-theory – Kusma Aug 26 '18 at 16:56
  • Did you create another account, or lose your login credentials? Anyway, this is explained in Bernard¨s answer to the linked question. – Jyrki Lahtonen Aug 26 '18 at 17:27
  • Also, (assuming you are a new user, say a class mate of the earlier asker) please check out our guide to new askers. The question is a bit lacking in context. No thoughts of your own. No indication as to the level, and hence no idea what tools you have mastered. Hint You know a polynomial with roots $a,b,c$. If $Ax^3+Bx^2+Cx+D=0$ whenever $x=a,b,c$, then also $Ax^{m+3}+Bx^{m+2}+Cx^{m+1}+Dx^m=0$. – Jyrki Lahtonen Aug 26 '18 at 17:32

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