7th Balkan 1990 Problem 4 The function f is defined on the positive integers and f(m) ≠ f(n) if m - n is prime. What is the smallest possible size of the image of f. Solution
: 4. f(1), f(3), f(6), f(8) must all be different. So the image must contain at least 4 elements. But the example f(n) = residue of n mod 4 shows that 4 is sufficient. 7th Balkan 1990 © John Scholes jscholes@kalva.demon.co.uk 11 Apr 2002