Let f define such as f(1)=1,f(3)=3 ∀ n≥2 , f(2n)=f(n) f(4n+1)=2f(2n+1)−f(n) f(4n+3)=3f(2n+1)−2f(n) 1)Prove that ∀ n , f(n) is odd 2)Prove that if f(a_n )=a_n , then a_n =2^n −1 or a


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Question Number 139323 by snipers237 last updated on 25/Apr/21

$L e t f d e f i n e s u c h a s f (1) = 1, f (3) = 3$ $\forall n ⩾ 2, f (2 n) = f (n)$ $f (4 n + 1) = 2 f (2 n + 1) - f (n)$ $f (4 n + 3) = 3 f (2 n + 1) - 2 f (n)$ $1) P r o v e t h a t \forall n, f (n) i s o d d$ $2) P r o v e t h a t i f f (a_{n}) = a_{n},$ $t h e n a_{n} = 2^{n} - 1 o r a_{n} = 2^{n} + 1$
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