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Omni-MATH / Let N={1,2,3,…}. Determine if there exists a strictly increasing function f: mathbb{N} mapsto mathbb{N} with the following properties: (i) f(1)=2; (ii) f(f(n))=f(n)+n,(n∈N).

Problem

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problem

Let N={1,2,3,…}\mathbb{N} = \{1,2,3, \ldots\}. Determine if there exists a strictly increasing function $f: \mathbb{N} \mapsto \mathbb{N}$ with the following properties: (i) f(1)=2f(1) = 2; (ii) f(f(n))=f(n)+n,(n∈N)f(f(n)) = f(n) + n, (n \in \mathbb{N}).
Plain-text mathematical notation (without MathML)
Let N={1,2,3,…}. Determine if there exists a strictly increasing function $f: \mathbb{N} \mapsto \mathbb{N}$ with the following properties:

(i) f(1)=2;

(ii) f(f(n))=f(n)+n,(n∈N).
Original LaTeX notation
Let $\mathbb{N} = \{1,2,3, \ldots\}$. Determine if there exists a strictly increasing function $f: \mathbb{N} \mapsto \mathbb{N}$ with the following properties:

(i) $f(1) = 2$;

(ii) $f(f(n)) = f(n) + n, (n \in \mathbb{N})$.

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Source and history

task_id
ea2775e5-fb1c-5b92-ae44-007bd7420126
task_key
test--ea2775e5-fb1c-5b92-ae44-007bd7420126
task_revision_id
1
config / split
/ test

Official source

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