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Omni-MATH / Let f:N→N be a function satisfying the following conditions: (1) f(1)=1; (2) ∀n∈N, 3f(n)f(2n+1)=f(2n)(1+3f(n)); (3) ∀n∈N, f(2n)<6f(n). Find all solutions of equation f(k)+f(l)=293,…

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problem

Let f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} be a function satisfying the following conditions: (1) f(1)=1f(1)=1; (2) ∀n∈N\forall n\in \mathbb{N}, 3f(n)f(2n+1)=f(2n)(1+3f(n))3f(n) f(2n+1) =f(2n) ( 1+3f(n) ); (3) ∀n∈N\forall n\in \mathbb{N}, f(2n)<6f(n)f(2n) < 6 f(n). Find all solutions of equation f(k)+f(l)=293f(k) +f(l)=293, where k<lk<l. (N\mathbb{N} denotes the set of all natural numbers).
Plain-text mathematical notation (without MathML)
Let f:N→N be a function satisfying the following conditions:
(1) f(1)=1;
(2) ∀n∈N, 3f(n)f(2n+1)=f(2n)(1+3f(n));
(3) ∀n∈N, f(2n)<6f(n).
Find all solutions of equation f(k)+f(l)=293, where k<l.
(N denotes the set of all natural numbers).
Original LaTeX notation
Let $f: \mathbb{N} \rightarrow \mathbb{N}$ be a function satisfying the following conditions:
(1) $f(1)=1$;
(2) $\forall n\in \mathbb{N}$, $3f(n) f(2n+1) =f(2n) ( 1+3f(n) )$;
(3) $\forall n\in \mathbb{N}$, $f(2n) < 6 f(n)$.
Find all solutions of equation $f(k) +f(l)=293$, where $k<l$.
($\mathbb{N}$ denotes the set of all natural numbers).

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Source and history

task_id
13d65ac7-0bf0-571a-b0a6-b73b2e6f1df0
task_key
test--13d65ac7-0bf0-571a-b0a6-b73b2e6f1df0
task_revision_id
5
config / split
/ test

Official source

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