Another functional equation

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October 19th 2008, 06:37 AM
alexmahone

Another functional equation

Let $X$ be the set of all positive integers greater than or equal to $8$ and let $f: X \to X$ be a function such that $f(x + y) = f(xy)$ for all $x \ge 4, y \ge 4$ . If $f(8) = 9$ , determine $f(9)$ .
October 19th 2008, 08:25 AM
Moo

Hello,

Quote:

Originally Posted by alexmahone

Let $X$ be the set of all positive integers greater than or equal to $8$ and let $f: X \to X$ be a function such that $f(x + y) = f(xy)$ for all $x \ge 4, y \ge 4$ . If $f(8) = 9$ , determine $f(9)$ .

$f(9)=f(5+4)=f(20)=f(16+4)=f(64)$

$f(8)=f(4+4)=f(16)=f(8+8)=f(64)$

Hence $f(8)=f(9)$

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