Mathegoras

Functions › Functional equations › Extremes in functional equations

Threshold of a functional equation

University · ●●●○○ 50 pts

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 mm with n≥m+1n \ge m + 1. Find the smallest nonnegative integer nn such that f(n)>106f(n) > 10^6.

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