Given-u-0-5-u-n-1-3u-n-4-1-show-that-n-N-u-n-2-3-u-n-1-a-Deduct-that-u-n-is-odd-c-Show-that-GCD-u-n-u-n-1-1-d-Deduct-GCD-6-3-1002-6-3-1003-GCD-greate

Question Number 124682 by mathocean1 last updated on 05/Dec/20

G i v e n {\begin{cases} u_{0} = 5 \\ u_{n + 1} = 3 u_{n} - 4 \end{cases}

1 . s h o w t h a t \forall n \in N, u_{n} = 2 + 3^{u_{n + 1}}

a . D e d u c t t h a t u_{n} i s o d d .

c . S h o w t h a t G C D (u_{n}; u_{n + 1}) = 1

d . D e d u c t G C D (6 + 3^{1002}; 6 + 3^{1003}) .

G C D = g r e a t e s t c o m m o n {d i v i s o r}^{}