A problem on recursive functions

Question

Given the function,

$$f(n)= \begin{cases} \ n-3 \quad \text{ if }\quad n\ge1000\\ \\ f (f (n+5)) \quad\text{ if } \quad n<1000 \end{cases} $$

What is the value of $f (83)-f (84) $?

One of my friends gave me this problem. I tried to find a pattern for the numbers but couldn't. I programmed the recursive function on C++ and got $1$ as the answer.

Your program constitutes a mathematical proof. – conditionalMethod Oct 21 '19 at 13:37 — conditionalMethod, Oct 21 '19 at 13:37

score 2 · Accepted Answer · answered Oct 21 '19 at 14:28

2

Hint: Prove by induction that $f(n)=997+(n \bmod 2)$ for $n<1000$. (Actually, for $n\le 1001$.)

answered Oct 21 '19 at 14:28

lhf

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A problem on recursive functions

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