let f function from z to z(integers)

and

f(n)=n - 3 at n > 999

f(n)= f(f(n+5) at n < 1000

find

f(84)

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- Jun 27th 2007, 11:07 AM #1

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- Jun 27th 2007, 11:46 AM #2

- Jun 30th 2007, 06:46 PM #3

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Note that,

for is determined by the parity of .

Meaning if is odd. And if is even.

We can show this by*Strong Induction*.

First,

Now, if and odd we have,

But by induction and the fact is even

And, if and even we have,

But by induction and the fact is odd

The above gives us an explicit formula for f(n).