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MATH / Let f be a function taking the nonnegative integers to the positive integers such that f(0)=f(1)=1 and (f(n)f(m+1))/(f(m))+(f(n)f(n−m))/(f(n−m−1))=f(n+1)for all nonnegative integer…

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problem

Let ff be a function taking the nonnegative integers to the positive integers such that f(0)=f(1)=1f(0) = f(1) = 1 and f(n)f(m+1)f(m)+f(n)f(n−m)f(n−m−1)=f(n+1)\frac{f(n) f(m + 1)}{f(m)} + \frac{f(n) f(n - m)}{f(n - m - 1)} = f(n + 1)for all nonnegative integers nn and m,m, where n≥m+1.n \ge m + 1. Find the smallest nonnegative integer nn such that f(n)>106.f(n) > 10^6.
Plain-text mathematical notation (without MathML)
Let f be a function taking the nonnegative integers to the positive integers such that f(0)=f(1)=1 and
(f(n)f(m+1))/(f(m))+(f(n)f(n−m))/(f(n−m−1))=f(n+1)for all nonnegative integers n and m, where n≥m+1.

Find the smallest nonnegative integer n such that f(n)>10⁶.
Original LaTeX notation
Let $f$ be a function taking the nonnegative integers to the positive integers such that $f(0) = f(1) = 1$ and
\[\frac{f(n) f(m + 1)}{f(m)} + \frac{f(n) f(n - m)}{f(n - m - 1)} = f(n + 1)\]for all nonnegative integers $n$ and $m,$ where $n \ge m + 1.$

Find the smallest nonnegative integer $n$ such that $f(n) > 10^6.$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
51050949-62d8-5570-9287-decee9ac49b5
task_key
intermediate~5falgebra--test--51050949-62d8-5570-9287-decee9ac49b5
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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