For-real-numbers-a-b-c-define-s-n-a-n-b-n-c-n-Suppose-s-1-2-s-2-6-and-s-3-14-Prove-that-s-n-2-s-n-1-s-n-1-8-holds-n-gt-1-

Question Number 123595 by Snail last updated on 26/Nov/20

F o r r e a l n u m b e r s (a / b / c) d e f i n e s_{n} = a^{n} + b^{n} + c^{n}

S u p p o s e s_{1} = 2 s_{2} = 6 a n d s_{3} = 14 . P r o v e t h a t

∣ s_{n}^{2} - s_{n - 1} s_{n + 1} ∣= 8 = h o l d s \forall n > 1

Commented by Snail last updated on 26/Nov/20

I h a d t r i e d u s i n g M a t h e m a t i c a l I n d u c t i o n b u t u n a b l d t o s o l v e

Facebook Tweet Pin