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Problem 7 of RMO 2006 (Regional Mathematical Olympiad-India)

Source: Functional Equation

September 13, 2009
functionsearchalgebra unsolvedalgebra

Problem Statement

Let X X be the set of all positive integers greater than or equal to 8 8 and let f:X→X f: X\rightarrow X be a function such that f(x\plus{}y)\equal{}f(xy) for all x≥4,y≥4. x\ge 4, y\ge 4 . if f(8)\equal{}9, determine f(9). f(9) .
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